Stability Analysis of the Euler Discretization for SIR Epidemic Model

Size: px
Start display at page:

Download "Stability Analysis of the Euler Discretization for SIR Epidemic Model"

Transcription

1 Stability Aalysis of the Euler Discretizatio for SIR Epidemic Model Agus Suryato Departmet of Mathematics, Faculty of Scieces, Brawijaya Uiversity, Jl Vetera Malag 6545 Idoesia Abstract I this paper we cosider a discrete SIR epidemic model obtaied by the Euler method For that discrete model, existece of disease free equilibrium ad edemic equilibrium is established Sufficiet coditios o the local asymptotical stability of both disease free equilibrium ad edemic equilibrium are also derived It is foud that the local asymptotical stability of the existig equilibrium is achieved oly for a small time step size h If h is further icreased ad passes the critical value, the both equilibriums will lose their stability Our umerical simulatios show that a complex dyamical behavior such as bifurcatio or chaos pheomeo will appear for relatively large h Both aalytical ad umerical results show that the discrete SIR model has a richer dyamical behavior tha its cotiuous couterpart Keywords: Discrete SIR epidemic model, Euler method, Stability aalysis, Bifurcatio diagram PACS: 87Ed, 6Lj, 545-a INTRODUCTION Mathematical models that describe dyamical behavior of ifectious diseases trasmissios have bee extesively studied [-] Such mathematical modelsare usually writte assystem of oliear differetial equatiosoe of basic epidemic model divides the total populatio ito three classes: susceptible idividuals(s), ifective idividuals (I)ad idividuals who have recovered or who have the disease but o loger ifective (R) By assumig that the recovered idividuals will acquire life-log immuity,we obtai the well-kow SIR epidemic model: ds S SI di SI I dr I R, where the positive time-ivariat parameters,,, ad are the recruitmet (birth ad immigratio) rate, the atural death rate, the trasmissio disease coefficiet, the rate of recovery from disease ad the rate of death iduced by the disease, respectivelythe dyamics of model () are well uderstood The basic reproductio umber for system () is System () has always a disease free equilibrium (DFE) poit /,, E Furthermore, if the system () also has a edemic equilibrium (EE) poit E Se, Ie, Re, where S, e Ie ad R e The DFE poit is asymptotically stable if, while the EE poit is asymptotically stable wheever For practical purposes, for example due to the eed of scietific computatio ad realtimesimulatio, the cotiuous model has to be solved umerically Oe of the commo method for solvig a system of oliear () Proceedigs of the 3rd Iteratioal Coferece o Mathematical Scieces AIP Cof Proc 6, (4); doi: 63/ AIP Publishig LLC /$3 375 This article is copyrighted as idicated i the article Reuse of AIP cotet is subject to the terms at: Dowloaded to IP: O: Wed, 8 Oct 4 8::

2 differetial equatios is Euler method [3-5, 7] or ostadard fiite differece method [6, 8-]I this paper, the cotiuous model () will be discretized usig theforward Euler scheme to get whereh is the time step size, f t I h S S h h h I S R hi h h R, I f ad t h,,,, We focus o the behaviors ofdiscrete dyamical system () The discrete system () is cosidered i [3] but oly for the case of uit time step, ie whe h = For this case, they derived sufficiet coditios for the global stability of the existig equilibrium The case of arbitrary time step h has bee studied i [4,5], but oly for the case of Here we study the dyamics of discrete system () for arbitrary time step had Specifically, we aim to derive the coditio for the local stabilityof the existig equilibrium We are also iterested i the dyamics of system () whe a equilibrium losses its stability () EQUILIBRIUM POINT AND ITS STABILITY Equilibrium Poits Equilibrium poits of discrete system () ca be foud by substitutig S S S ; I I I ; ad R R R ito () ad solvig the resultig system of equatios We fid that there always exists a DFE poit E /,,Furthermore, if the we also have a EE poit E Se, Ie, Re Therefore the equilibrium poits of discrete system () are cosistet with those of the cotiuous model () I the followig we study the local stability of each equilibrium poit by cosiderig the liearizatio of system () at the DFE poit ad E S, I, R is EE poit, respectively The Jacobia matrix of the liearized system at equilibrium J h hi hs h E hi hs h (3) Equilibrium E is asymptotically stable if the modulus of all eigevalues of the correspodig Jacobia matrix J E are less tha oe Stability of Disease Free Equilibrium The characteristic equatio of the Jacobia matrix (3) at the DFE poit E /,, The eigevalues of E h h (4) h ad J are h 3 h / It is clear that if h / It ca also be show that 3 if ad h / Hece, we have the followig theorem is 376 This article is copyrighted as idicated i the article Reuse of AIP cotet is subject to the terms at: Dowloaded to IP: O: Wed, 8 Oct 4 8::

3 Theorem The disease free equilibrium /,, E is asymptotically stable if ad h mi, At the edemic equilibrium poit E S I, R Stability of Edemic Equilibrium e, e e, the Jacobia matrix (3) has the followig characteristic equatio h A B (5) where h B h h Clearly that oe of the eigevalues of the Jacobia matrix is h while other eigevalues, 3are determied by A B if h / The modulus of other eigevalues will be studied usig the followig lemma A ad Lemma [6, ] The quadratic equatio A B has two roots that satisfy i, i, 3 if ad oly if the followig coditios are satisfied: (i) B, (ii) A B, (iii) A B From equatio (5), it ca be show that coditio B ad A B are respectively equivalet to h ad The coditio A B is the same as h h 4 By deotig D 4 6 we cosider three cases as follow: Case i: Suppose that D, the A B is satisfied if h Case ii: Suppose that D, the A B holds if Case iii: Suppose that D, the A B holds if h h D or D h Based o the above discussio, we obtai the followig theorem Theorem 3 The edemic equilibrium poit S I, R coditios holds: E is asymptotically stable if ad oe of the followig e, e e 377 This article is copyrighted as idicated i the article Reuse of AIP cotet is subject to the terms at: Dowloaded to IP: O: Wed, 8 Oct 4 8::

4 () D ad () D ad h mi, mi,, D h We remark that the stability aalysis of discrete model () with has bee discussed i [4] Here, the author used differet method whe ivestigatig the properties of the eigevalues of Jacobia matrix Nevertheless, for the case of, the coditios for both DFE poit ad EE poit to be asymptotically stable give by Theorem ad Theorem are i accordace with the coditios give i [4] NUMERICAL SIMULATIONS FIGURE Susceptible idividuals as fuctio of time calculated usig scheme () for differet values of h To illustrate the behavior of discrete SIR epidemic model (), we perform some umerical simulatios usig 445,, 5, 5, ad varyig the value of time step h Usig those parameters, we have 5669, E 5,,, 4,58676,4669 previous aalysis, the EE poit 4, 58676,4669 E ad D Accordig to the E is asymptotically stable if h 987 I Figure, we show our umerical results usig h 9, 9,, ad iitial value S () 39, I 5 7 This plot shows the umber of susceptible idividuals as fuctio of time It is show that if we take h 9, the the solutio is coverget to the EE poit as expected However, if we use h 987 the the EE poit loses its stability I particular, if we choose h 9,, the the umerical solutio shows that there exists -periodic, 4-periodic ad 8-periodic solutio, respectively Takig higher value of h leads to solutio with chaotic behavior Such a behavior ca be see from the bifurcatio diagram as show i Figure Chaos occurs i the bads where the dotsseem to be smeared at radom This diagram shows that the discrete model () has richer dyamics compared to the origial cotiuous model () 378 This article is copyrighted as idicated i the article Reuse of AIP cotet is subject to the terms at: Dowloaded to IP: O: Wed, 8 Oct 4 8::

5 FIGURE Bifurcatio diagram CONCLUDING REMARKS We have aalyzed a discrete SIR epidemic model obtaied from the Euler scheme It is show that the stability of both DFE poit ad EE poit of the discrete system is cosistet with its origial cotiuous model oly if a relatively small time step (h) is used For relatively large time step, both equilibrium poits may lose their stability ad may show complex dyamical behavior Mathematically, such behavior is iterestig but it is ot dyamically cosistet with its related cotiuous model Therefore, we suggest usig other umerical methods whe solvig the SIR system, for example ostadard fiite differece method ACKNOWLEDGMENTS This research is fiacially supported by the Directorate Geeral of Higher Educatio, Miistry of Educatio ad Culture of Republic Idoesia via DIPA of Brawijaya Uiversity No:DIPA /3, ad based o letter of decisio of Brawijaya Uiversity Rector No: 95/SK/3 REFERENCES F Brauer ad C Castillo-Chavez, Mathematical models i populatio biology ad epidemiology, New York: Spriger- Verlag, HW Hethcote, SIAM Rev 4, () 3 X Ma, Y Zhou ad H Cao, Advaces i Differece Equatios 3, 4 (3) 4 W Piyawog, Spatio-Temporal Numerical Modellig of Whoopig Cough Dyamics, PhD Thesis, Bruel Uiversity, 5 Z Hu, Z Teg ad H Jiag, Noliear Aalysis: Real World Applicatios 3(5), 7 33 () 6 MY Ogu ad I Turha, Joural of Applied Mathematics 3, 9 (3) 7 T Fayeldi, A Suryato ad A Widodo, It J Appl Math Stat 47 (7), (3) 8 RE Mickes, Applicatio of ostadard fiite differece schemes, Sigapore: World Scietific Publishig Co Pte Ltd, 9 RE Mickes, Nostadard Fiite Differece Models of Differetial Equatios, Sigapore: World Scietific, 994 A Suryato, It J MathComput 3 (D), -3 () A Suryato, WM Kusumawiahyu, I Darti ad I Yati, Comput Appl Math 3(), (3) S Elaydi, A itroductio to differece equatios, New York: Spriger, This article is copyrighted as idicated i the article Reuse of AIP cotet is subject to the terms at: Dowloaded to IP: O: Wed, 8 Oct 4 8::

Dominant of Functions Satisfying a Differential Subordination and Applications

Dominant of Functions Satisfying a Differential Subordination and Applications Domiat of Fuctios Satisfyig a Differetial Subordiatio ad Applicatios R Chadrashekar a, Rosiha M Ali b ad K G Subramaia c a Departmet of Techology Maagemet, Faculty of Techology Maagemet ad Busiess, Uiversiti

More information

Comparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series

Comparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series Applied Mathematical Scieces, Vol. 7, 03, o. 6, 3-337 HIKARI Ltd, www.m-hikari.com http://d.doi.org/0.988/ams.03.3430 Compariso Study of Series Approimatio ad Covergece betwee Chebyshev ad Legedre Series

More information

AN OPEN-PLUS-CLOSED-LOOP APPROACH TO SYNCHRONIZATION OF CHAOTIC AND HYPERCHAOTIC MAPS

AN OPEN-PLUS-CLOSED-LOOP APPROACH TO SYNCHRONIZATION OF CHAOTIC AND HYPERCHAOTIC MAPS http://www.paper.edu.c Iteratioal Joural of Bifurcatio ad Chaos, Vol. 1, No. 5 () 119 15 c World Scietific Publishig Compay AN OPEN-PLUS-CLOSED-LOOP APPROACH TO SYNCHRONIZATION OF CHAOTIC AND HYPERCHAOTIC

More information

Dynamical Behavior of High-order Rational Difference System

Dynamical Behavior of High-order Rational Difference System WSEAS TRANSACTIONS o MATHEMATICS Qiahog Zhag Wezhua Zhag Dyamical Behavior of High-order Ratioal Differece System Qiahog Zhag Guizhou Uiversity of Fiace ad Ecoomics School of Mathematics ad Statistics

More information

Research Article Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems

Research Article Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems Abstract ad Applied Aalysis Volume 203, Article ID 39868, 6 pages http://dx.doi.org/0.55/203/39868 Research Article Noexistece of Homocliic Solutios for a Class of Discrete Hamiltoia Systems Xiaopig Wag

More information

A NEW CLASS OF 2-STEP RATIONAL MULTISTEP METHODS

A NEW CLASS OF 2-STEP RATIONAL MULTISTEP METHODS Jural Karya Asli Loreka Ahli Matematik Vol. No. (010) page 6-9. Jural Karya Asli Loreka Ahli Matematik A NEW CLASS OF -STEP RATIONAL MULTISTEP METHODS 1 Nazeeruddi Yaacob Teh Yua Yig Norma Alias 1 Departmet

More information

Modified Decomposition Method by Adomian and. Rach for Solving Nonlinear Volterra Integro- Differential Equations

Modified Decomposition Method by Adomian and. Rach for Solving Nonlinear Volterra Integro- Differential Equations Noliear Aalysis ad Differetial Equatios, Vol. 5, 27, o. 4, 57-7 HIKARI Ltd, www.m-hikari.com https://doi.org/.2988/ade.27.62 Modified Decompositio Method by Adomia ad Rach for Solvig Noliear Volterra Itegro-

More information

μ are complex parameters. Other

μ are complex parameters. Other A New Numerical Itegrator for the Solutio of Iitial Value Problems i Ordiary Differetial Equatios. J. Suday * ad M.R. Odekule Departmet of Mathematical Scieces, Adamawa State Uiversity, Mubi, Nigeria.

More information

Research Article A New Second-Order Iteration Method for Solving Nonlinear Equations

Research Article A New Second-Order Iteration Method for Solving Nonlinear Equations Abstract ad Applied Aalysis Volume 2013, Article ID 487062, 4 pages http://dx.doi.org/10.1155/2013/487062 Research Article A New Secod-Order Iteratio Method for Solvig Noliear Equatios Shi Mi Kag, 1 Arif

More information

Research Article Nonautonomous Discrete Neuron Model with Multiple Periodic and Eventually Periodic Solutions

Research Article Nonautonomous Discrete Neuron Model with Multiple Periodic and Eventually Periodic Solutions Discrete Dyamics i Nature ad Society Volume 21, Article ID 147282, 6 pages http://dx.doi.org/1.11/21/147282 Research Article Noautoomous Discrete Neuro Model with Multiple Periodic ad Evetually Periodic

More information

MATHEMATICAL MODELS - Vol. I - Controllability, Observability, and Stability of Mathematical Models - Abderrahman Iggidr

MATHEMATICAL MODELS - Vol. I - Controllability, Observability, and Stability of Mathematical Models - Abderrahman Iggidr CONTROLLABILITY, OBSERVABILITY, AND STABILITY OF MATHEMATICAL MODELS Abderrahma Iggidr INRIA (Ur Lorraie) ad, Uiversity of Metz, Frace Keywords: accessibility, asymptotic stability, attractivity, chemostat,

More information

DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS. Park Road, Islamabad, Pakistan

DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS. Park Road, Islamabad, Pakistan Mathematical ad Computatioal Applicatios, Vol. 9, No. 3, pp. 30-40, 04 DECOMPOSITION METHOD FOR SOLVING A SYSTEM OF THIRD-ORDER BOUNDARY VALUE PROBLEMS Muhammad Aslam Noor, Khalida Iayat Noor ad Asif Waheed

More information

Taylor polynomial solution of difference equation with constant coefficients via time scales calculus

Taylor polynomial solution of difference equation with constant coefficients via time scales calculus TMSCI 3, o 3, 129-135 (2015) 129 ew Treds i Mathematical Scieces http://wwwtmscicom Taylor polyomial solutio of differece equatio with costat coefficiets via time scales calculus Veysel Fuat Hatipoglu

More information

Chapter 4. Fourier Series

Chapter 4. Fourier Series Chapter 4. Fourier Series At this poit we are ready to ow cosider the caoical equatios. Cosider, for eample the heat equatio u t = u, < (4.) subject to u(, ) = si, u(, t) = u(, t) =. (4.) Here,

More information

Some properties of Boubaker polynomials and applications

Some properties of Boubaker polynomials and applications Some properties of Boubaker polyomials ad applicatios Gradimir V. Milovaović ad Duša Joksimović Citatio: AIP Cof. Proc. 179, 1050 (2012); doi: 10.1063/1.756326 View olie: http://dx.doi.org/10.1063/1.756326

More information

Fixed Point Theorems for Expansive Mappings in G-metric Spaces

Fixed Point Theorems for Expansive Mappings in G-metric Spaces Turkish Joural of Aalysis ad Number Theory, 7, Vol. 5, No., 57-6 Available olie at http://pubs.sciepub.com/tjat/5//3 Sciece ad Educatio Publishig DOI:.69/tjat-5--3 Fixed Poit Theorems for Expasive Mappigs

More information

Finite Difference Approximation for Transport Equation with Shifts Arising in Neuronal Variability

Finite Difference Approximation for Transport Equation with Shifts Arising in Neuronal Variability Iteratioal Joural of Sciece ad Research (IJSR) ISSN (Olie): 39-764 Ide Copericus Value (3): 64 Impact Factor (3): 4438 Fiite Differece Approimatio for Trasport Equatio with Shifts Arisig i Neuroal Variability

More information

Stopping oscillations of a simple harmonic oscillator using an impulse force

Stopping oscillations of a simple harmonic oscillator using an impulse force It. J. Adv. Appl. Math. ad Mech. 5() (207) 6 (ISSN: 2347-2529) IJAAMM Joural homepage: www.ijaamm.com Iteratioal Joural of Advaces i Applied Mathematics ad Mechaics Stoppig oscillatios of a simple harmoic

More information

Research Article Two Expanding Integrable Models of the Geng-Cao Hierarchy

Research Article Two Expanding Integrable Models of the Geng-Cao Hierarchy Abstract ad Applied Aalysis Volume 214, Article ID 86935, 7 pages http://d.doi.org/1.1155/214/86935 Research Article Two Epadig Itegrable Models of the Geg-Cao Hierarchy Xiurog Guo, 1 Yufeg Zhag, 2 ad

More information

Finite Difference Approximation for First- Order Hyperbolic Partial Differential Equation Arising in Neuronal Variability with Shifts

Finite Difference Approximation for First- Order Hyperbolic Partial Differential Equation Arising in Neuronal Variability with Shifts Iteratioal Joural of Scietific Egieerig ad Research (IJSER) wwwiseri ISSN (Olie): 347-3878, Impact Factor (4): 35 Fiite Differece Approimatio for First- Order Hyperbolic Partial Differetial Equatio Arisig

More information

Benaissa Bernoussi Université Abdelmalek Essaadi, ENSAT de Tanger, B.P. 416, Tanger, Morocco

Benaissa Bernoussi Université Abdelmalek Essaadi, ENSAT de Tanger, B.P. 416, Tanger, Morocco EXTENDING THE BERNOULLI-EULER METHOD FOR FINDING ZEROS OF HOLOMORPHIC FUNCTIONS Beaissa Beroussi Uiversité Abdelmalek Essaadi, ENSAT de Tager, B.P. 416, Tager, Morocco e-mail: Beaissa@fstt.ac.ma Mustapha

More information

Chapter 2: Numerical Methods

Chapter 2: Numerical Methods Chapter : Numerical Methods. Some Numerical Methods for st Order ODEs I this sectio, a summar of essetial features of umerical methods related to solutios of ordiar differetial equatios is give. I geeral,

More information

Chapter 2 The Solution of Numerical Algebraic and Transcendental Equations

Chapter 2 The Solution of Numerical Algebraic and Transcendental Equations Chapter The Solutio of Numerical Algebraic ad Trascedetal Equatios Itroductio I this chapter we shall discuss some umerical methods for solvig algebraic ad trascedetal equatios. The equatio f( is said

More information

ON SOME DIOPHANTINE EQUATIONS RELATED TO SQUARE TRIANGULAR AND BALANCING NUMBERS

ON SOME DIOPHANTINE EQUATIONS RELATED TO SQUARE TRIANGULAR AND BALANCING NUMBERS Joural of Algebra, Number Theory: Advaces ad Applicatios Volume, Number, 00, Pages 7-89 ON SOME DIOPHANTINE EQUATIONS RELATED TO SQUARE TRIANGULAR AND BALANCING NUMBERS OLCAY KARAATLI ad REFİK KESKİN Departmet

More information

Asymptotic Behaviour of Solutions of Certain Third Order Nonlinear Differential Equations via Phase Portrait Analysis

Asymptotic Behaviour of Solutions of Certain Third Order Nonlinear Differential Equations via Phase Portrait Analysis Applied Mathematics, 6, 7, 34-335 http://wwwscirporg/joural/am ISSN Olie: 5-7393 ISSN Prit: 5-7385 Asymptotic Behaviour of Solutios of Certai Third Order Noliear Differetial Equatios via Phase Portrait

More information

Numerical Solutions of Second Order Boundary Value Problems by Galerkin Residual Method on Using Legendre Polynomials

Numerical Solutions of Second Order Boundary Value Problems by Galerkin Residual Method on Using Legendre Polynomials IOSR Joural of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 319-765X. Volume 11, Issue 6 Ver. IV (Nov. - Dec. 15), PP 1-11 www.iosrjourals.org Numerical Solutios of Secod Order Boudary Value Problems

More information

Five Steps Block Predictor-Block Corrector Method for the Solution of ( )

Five Steps Block Predictor-Block Corrector Method for the Solution of ( ) Applied Mathematics, 4,, -66 Published Olie May 4 i SciRes. http://www.scirp.org/oural/am http://dx.doi.org/.46/am.4.87 Five Steps Block Predictor-Block Corrector y = f x, y, y Method for the Solutio of

More information

Analytical solutions for multi-wave transfer matrices in layered structures

Analytical solutions for multi-wave transfer matrices in layered structures Joural of Physics: Coferece Series PAPER OPEN ACCESS Aalytical solutios for multi-wave trasfer matrices i layered structures To cite this article: Yu N Belyayev 018 J Phys: Cof Ser 109 01008 View the article

More information

Application of Homotopy Perturbation Method for the Large Angle period of Nonlinear Oscillator

Application of Homotopy Perturbation Method for the Large Angle period of Nonlinear Oscillator Applicatio of Homotopy Perturbatio Method for the Large Agle period of Noliear Oscillator Olayiwola, M. O. Gbolagade A.W., Adesaya A.O. & Akipelu F.O. Departmet of Mathematical Scieces, Faculty of Sciece,

More information

A collocation method for singular integral equations with cosecant kernel via Semi-trigonometric interpolation

A collocation method for singular integral equations with cosecant kernel via Semi-trigonometric interpolation Iteratioal Joural of Mathematics Research. ISSN 0976-5840 Volume 9 Number 1 (017) pp. 45-51 Iteratioal Research Publicatio House http://www.irphouse.com A collocatio method for sigular itegral equatios

More information

PAijpam.eu ON TENSOR PRODUCT DECOMPOSITION

PAijpam.eu ON TENSOR PRODUCT DECOMPOSITION Iteratioal Joural of Pure ad Applied Mathematics Volume 103 No 3 2015, 537-545 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://wwwijpameu doi: http://dxdoiorg/1012732/ijpamv103i314

More information

MATH 10550, EXAM 3 SOLUTIONS

MATH 10550, EXAM 3 SOLUTIONS MATH 155, EXAM 3 SOLUTIONS 1. I fidig a approximate solutio to the equatio x 3 +x 4 = usig Newto s method with iitial approximatio x 1 = 1, what is x? Solutio. Recall that x +1 = x f(x ) f (x ). Hece,

More information

Exact Solutions for a Class of Nonlinear Singular Two-Point Boundary Value Problems: The Decomposition Method

Exact Solutions for a Class of Nonlinear Singular Two-Point Boundary Value Problems: The Decomposition Method Exact Solutios for a Class of Noliear Sigular Two-Poit Boudary Value Problems: The Decompositio Method Abd Elhalim Ebaid Departmet of Mathematics, Faculty of Sciece, Tabuk Uiversity, P O Box 741, Tabuki

More information

Notes on iteration and Newton s method. Iteration

Notes on iteration and Newton s method. Iteration Notes o iteratio ad Newto s method Iteratio Iteratio meas doig somethig over ad over. I our cotet, a iteratio is a sequece of umbers, vectors, fuctios, etc. geerated by a iteratio rule of the type 1 f

More information

ECE-S352 Introduction to Digital Signal Processing Lecture 3A Direct Solution of Difference Equations

ECE-S352 Introduction to Digital Signal Processing Lecture 3A Direct Solution of Difference Equations ECE-S352 Itroductio to Digital Sigal Processig Lecture 3A Direct Solutio of Differece Equatios Discrete Time Systems Described by Differece Equatios Uit impulse (sample) respose h() of a DT system allows

More information

NEW FAST CONVERGENT SEQUENCES OF EULER-MASCHERONI TYPE

NEW FAST CONVERGENT SEQUENCES OF EULER-MASCHERONI TYPE UPB Sci Bull, Series A, Vol 79, Iss, 207 ISSN 22-7027 NEW FAST CONVERGENT SEQUENCES OF EULER-MASCHERONI TYPE Gabriel Bercu We itroduce two ew sequeces of Euler-Mascheroi type which have fast covergece

More information

Period Function of a Lienard Equation

Period Function of a Lienard Equation Joural of Mathematical Scieces (4) -5 Betty Joes & Sisters Publishig Period Fuctio of a Lieard Equatio Khalil T Al-Dosary Departmet of Mathematics, Uiversity of Sharjah, Sharjah 77, Uited Arab Emirates

More information

(A sequence also can be thought of as the list of function values attained for a function f :ℵ X, where f (n) = x n for n 1.) x 1 x N +k x N +4 x 3

(A sequence also can be thought of as the list of function values attained for a function f :ℵ X, where f (n) = x n for n 1.) x 1 x N +k x N +4 x 3 MATH 337 Sequeces Dr. Neal, WKU Let X be a metric space with distace fuctio d. We shall defie the geeral cocept of sequece ad limit i a metric space, the apply the results i particular to some special

More information

The Sampling Distribution of the Maximum. Likelihood Estimators for the Parameters of. Beta-Binomial Distribution

The Sampling Distribution of the Maximum. Likelihood Estimators for the Parameters of. Beta-Binomial Distribution Iteratioal Mathematical Forum, Vol. 8, 2013, o. 26, 1263-1277 HIKARI Ltd, www.m-hikari.com http://d.doi.org/10.12988/imf.2013.3475 The Samplig Distributio of the Maimum Likelihood Estimators for the Parameters

More information

Analytic Theory of Probabilities

Analytic Theory of Probabilities Aalytic Theory of Probabilities PS Laplace Book II Chapter II, 4 pp 94 03 4 A lottery beig composed of umbered tickets of which r exit at each drawig, oe requires the probability that after i drawigs all

More information

Some New Iterative Methods for Solving Nonlinear Equations

Some New Iterative Methods for Solving Nonlinear Equations World Applied Scieces Joural 0 (6): 870-874, 01 ISSN 1818-495 IDOSI Publicatios, 01 DOI: 10.589/idosi.wasj.01.0.06.830 Some New Iterative Methods for Solvig Noliear Equatios Muhammad Aslam Noor, Khalida

More information

NEW IDENTIFICATION AND CONTROL METHODS OF SINE-FUNCTION JULIA SETS

NEW IDENTIFICATION AND CONTROL METHODS OF SINE-FUNCTION JULIA SETS Joural of Applied Aalysis ad Computatio Volume 5, Number 2, May 25, 22 23 Website:http://jaac-olie.com/ doi:.948/252 NEW IDENTIFICATION AND CONTROL METHODS OF SINE-FUNCTION JULIA SETS Jie Su,2, Wei Qiao

More information

A STUDY ON MHD BOUNDARY LAYER FLOW OVER A NONLINEAR STRETCHING SHEET USING IMPLICIT FINITE DIFFERENCE METHOD

A STUDY ON MHD BOUNDARY LAYER FLOW OVER A NONLINEAR STRETCHING SHEET USING IMPLICIT FINITE DIFFERENCE METHOD IRET: Iteratioal oural of Research i Egieerig ad Techology eissn: 39-63 pissn: 3-7308 A STUDY ON MHD BOUNDARY LAYER FLOW OVER A NONLINEAR STRETCHING SHEET USING IMPLICIT FINITE DIFFERENCE METHOD Satish

More information

IN many scientific and engineering applications, one often

IN many scientific and engineering applications, one often INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND APPLIED MATHEMATICS, VOL 3, NO, FEBRUARY 07 5 Secod Degree Refiemet Jacobi Iteratio Method for Solvig System of Liear Equatio Tesfaye Kebede Abstract Several

More information

IJITE Vol.2 Issue-11, (November 2014) ISSN: Impact Factor

IJITE Vol.2 Issue-11, (November 2014) ISSN: Impact Factor IJITE Vol Issue-, (November 4) ISSN: 3-776 ATTRACTIVITY OF A HIGHER ORDER NONLINEAR DIFFERENCE EQUATION Guagfeg Liu School of Zhagjiagag Jiagsu Uiversit of Sciece ad Techolog, Zhagjiagag, Jiagsu 56,PR

More information

MULTIPLE TIME SCALES SOLUTION OF AN EQUATION WITH QUADRATIC AND CUBIC NONLINEARITIES HAVING FRAC- TIONAL-ORDER DERIVATIVE

MULTIPLE TIME SCALES SOLUTION OF AN EQUATION WITH QUADRATIC AND CUBIC NONLINEARITIES HAVING FRAC- TIONAL-ORDER DERIVATIVE Mathematical ad Computatioal Applicatios, Vol. 6, No., pp. 3-38,. Associatio for Scietific Research MULIPLE IME SCALES SOLUION OF AN EQUAION WIH QUADRAIC AND CUBIC NONLINEARIIES HAVING FRAC- IONAL-ORDER

More information

Common Coupled Fixed Point of Mappings Satisfying Rational Inequalities in Ordered Complex Valued Generalized Metric Spaces

Common Coupled Fixed Point of Mappings Satisfying Rational Inequalities in Ordered Complex Valued Generalized Metric Spaces IOSR Joural of Mathematics (IOSR-JM) e-issn: 78-578, p-issn:319-765x Volume 10, Issue 3 Ver II (May-Ju 014), PP 69-77 Commo Coupled Fixed Poit of Mappigs Satisfyig Ratioal Iequalities i Ordered Complex

More information

62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 +

62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + 62. Power series Defiitio 16. (Power series) Give a sequece {c }, the series c x = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + is called a power series i the variable x. The umbers c are called the coefficiets of

More information

MATH 372: Difference Equations

MATH 372: Difference Equations MATH 372: Differece Equatios G. de Vries February 23, 2003 1 Itroductio I this chapter, we use discrete models to describe dyamical pheomea i biology. Discrete models are appropriate whe oe ca thik about

More information

The Differential Transform Method for Solving Volterra s Population Model

The Differential Transform Method for Solving Volterra s Population Model AASCIT Couicatios Volue, Issue 6 Septeber, 15 olie ISSN: 375-383 The Differetial Trasfor Method for Solvig Volterra s Populatio Model Khatereh Tabatabaei Departet of Matheatics, Faculty of Sciece, Kafas

More information

Mathematical Modeling of Optimum 3 Step Stress Accelerated Life Testing for Generalized Pareto Distribution

Mathematical Modeling of Optimum 3 Step Stress Accelerated Life Testing for Generalized Pareto Distribution America Joural of Theoretical ad Applied Statistics 05; 4(: 6-69 Published olie May 8, 05 (http://www.sciecepublishiggroup.com/j/ajtas doi: 0.648/j.ajtas.05040. ISSN: 6-8999 (Prit; ISSN: 6-9006 (Olie Mathematical

More information

PAijpam.eu ON DERIVATION OF RATIONAL SOLUTIONS OF BABBAGE S FUNCTIONAL EQUATION

PAijpam.eu ON DERIVATION OF RATIONAL SOLUTIONS OF BABBAGE S FUNCTIONAL EQUATION Iteratioal Joural of Pure ad Applied Mathematics Volume 94 No. 204, 9-20 ISSN: 3-8080 (prited versio); ISSN: 34-3395 (o-lie versio) url: http://www.ijpam.eu doi: http://dx.doi.org/0.2732/ijpam.v94i.2 PAijpam.eu

More information

CYCLING CHAOS IN ONE-DIMENSIONAL COUPLED ITERATED MAPS

CYCLING CHAOS IN ONE-DIMENSIONAL COUPLED ITERATED MAPS Letters Iteratioal Joural of Bifurcatio ad Chaos, Vol., No. 8 () 859 868 c World Scietific Publishig Compay CYCLING CHAOS IN ONE-DIMENSIONAL COUPLED ITERATED MAPS ANTONIO PALACIOS Departmet of Mathematics,

More information

Similarity Solutions to Unsteady Pseudoplastic. Flow Near a Moving Wall

Similarity Solutions to Unsteady Pseudoplastic. Flow Near a Moving Wall Iteratioal Mathematical Forum, Vol. 9, 04, o. 3, 465-475 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/imf.04.48 Similarity Solutios to Usteady Pseudoplastic Flow Near a Movig Wall W. Robi Egieerig

More information

Analysis and Numerical Approximation of a Singular Boundary Value Problem for the One-dimensional p-laplacian

Analysis and Numerical Approximation of a Singular Boundary Value Problem for the One-dimensional p-laplacian Proceedigs of the 4th WSEAS Iteratioal Coferece o Fluid Mechaics Gold Coast Queeslad Australia Jauary 7-9 007 4 Aalysis ad Numerical Approximatio of a Sigular Boudary Value Problem for the Oe-dimesioal

More information

Z - Transform. It offers the techniques for digital filter design and frequency analysis of digital signals.

Z - Transform. It offers the techniques for digital filter design and frequency analysis of digital signals. Z - Trasform The -trasform is a very importat tool i describig ad aalyig digital systems. It offers the techiques for digital filter desig ad frequecy aalysis of digital sigals. Defiitio of -trasform:

More information

Higher-order iterative methods by using Householder's method for solving certain nonlinear equations

Higher-order iterative methods by using Householder's method for solving certain nonlinear equations Math Sci Lett, No, 7- ( 7 Mathematical Sciece Letters A Iteratioal Joural http://dxdoiorg/785/msl/5 Higher-order iterative methods by usig Householder's method for solvig certai oliear equatios Waseem

More information

Massachusetts Institute of Technology

Massachusetts Institute of Technology 6.0/6.3: Probabilistic Systems Aalysis (Fall 00) Problem Set 8: Solutios. (a) We cosider a Markov chai with states 0,,, 3,, 5, where state i idicates that there are i shoes available at the frot door i

More information

On a class of convergent sequences defined by integrals 1

On a class of convergent sequences defined by integrals 1 Geeral Mathematics Vol. 4, No. 2 (26, 43 54 O a class of coverget sequeces defied by itegrals Dori Adrica ad Mihai Piticari Abstract The mai result shows that if g : [, ] R is a cotiuous fuctio such that

More information

Lainiotis filter implementation. via Chandrasekhar type algorithm

Lainiotis filter implementation. via Chandrasekhar type algorithm Joural of Computatios & Modellig, vol.1, o.1, 2011, 115-130 ISSN: 1792-7625 prit, 1792-8850 olie Iteratioal Scietific Press, 2011 Laiiotis filter implemetatio via Chadrasehar type algorithm Nicholas Assimais

More information

A New Hybrid in the Nonlinear Part of Adomian Decomposition Method for Initial Value Problem of Ordinary Differential Equation

A New Hybrid in the Nonlinear Part of Adomian Decomposition Method for Initial Value Problem of Ordinary Differential Equation Joural of Matematics Researc; Vol No ; ISSN - E-ISSN - Publised b Caadia Ceter of Sciece ad Educatio A New Hbrid i te Noliear Part of Adomia Decompositio Metod for Iitial Value Problem of Ordiar Differetial

More information

Modified Logistic Maps for Cryptographic Application

Modified Logistic Maps for Cryptographic Application Applied Mathematics, 25, 6, 773-782 Published Olie May 25 i SciRes. http://www.scirp.org/joural/am http://dx.doi.org/.4236/am.25.6573 Modified Logistic Maps for Cryptographic Applicatio Shahram Etemadi

More information

l -State Solutions of a New Four-Parameter 1/r^2 Singular Radial Non-Conventional Potential via Asymptotic Iteration Method

l -State Solutions of a New Four-Parameter 1/r^2 Singular Radial Non-Conventional Potential via Asymptotic Iteration Method America Joural of Computatioal ad Applied Mathematics 8, 8(): 7-3 DOI:.593/j.ajcam.88. l -State Solutios of a New Four-Parameter /r^ Sigular Radial No-Covetioal Potetial via Asymptotic Iteratio Method

More information

Time-Domain Representations of LTI Systems

Time-Domain Representations of LTI Systems 2.1 Itroductio Objectives: 1. Impulse resposes of LTI systems 2. Liear costat-coefficiets differetial or differece equatios of LTI systems 3. Bloc diagram represetatios of LTI systems 4. State-variable

More information

Stability of fractional positive nonlinear systems

Stability of fractional positive nonlinear systems Archives of Cotrol Scieces Volume 5(LXI), 15 No. 4, pages 491 496 Stability of fractioal positive oliear systems TADEUSZ KACZOREK The coditios for positivity ad stability of a class of fractioal oliear

More information

Research Article A Note on Ergodicity of Systems with the Asymptotic Average Shadowing Property

Research Article A Note on Ergodicity of Systems with the Asymptotic Average Shadowing Property Discrete Dyamics i Nature ad Society Volume 2011, Article ID 360583, 6 pages doi:10.1155/2011/360583 Research Article A Note o Ergodicity of Systems with the Asymptotic Average Shadowig Property Risog

More information

Sequences and Limits

Sequences and Limits Chapter Sequeces ad Limits Let { a } be a sequece of real or complex umbers A ecessary ad sufficiet coditio for the sequece to coverge is that for ay ɛ > 0 there exists a iteger N > 0 such that a p a q

More information

Uniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations

Uniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations Global Joural of Sciece Frotier Research Mathematics ad Decisio Scieces Volume 3 Issue Versio 0 Year 03 Type : Double Blid Peer Reviewed Iteratioal Research Joural Publisher: Global Jourals Ic (USA Olie

More information

Average Number of Real Zeros of Random Fractional Polynomial-II

Average Number of Real Zeros of Random Fractional Polynomial-II Average Number of Real Zeros of Radom Fractioal Polyomial-II K Kadambavaam, PG ad Research Departmet of Mathematics, Sri Vasavi College, Erode, Tamiladu, Idia M Sudharai, Departmet of Mathematics, Velalar

More information

Numerical integration of analytic functions

Numerical integration of analytic functions Numerical itegratio of aalytic fuctios Gradimir V. Milovaović, Dobrilo Ð Tošić, ad Miloljub Albijaić Citatio: AIP Cof. Proc. 1479, 146 212); doi: 1.163/1.4756325 View olie: http://dx.doi.org/1.163/1.4756325

More information

New Version of the Rayleigh Schrödinger Perturbation Theory: Examples

New Version of the Rayleigh Schrödinger Perturbation Theory: Examples New Versio of the Rayleigh Schrödiger Perturbatio Theory: Examples MILOŠ KALHOUS, 1 L. SKÁLA, 1 J. ZAMASTIL, 1 J. ČÍŽEK 2 1 Charles Uiversity, Faculty of Mathematics Physics, Ke Karlovu 3, 12116 Prague

More information

Streamfunction-Vorticity Formulation

Streamfunction-Vorticity Formulation Streamfuctio-Vorticity Formulatio A. Salih Departmet of Aerospace Egieerig Idia Istitute of Space Sciece ad Techology, Thiruvaathapuram March 2013 The streamfuctio-vorticity formulatio was amog the first

More information

Research Article Some E-J Generalized Hausdorff Matrices Not of Type M

Research Article Some E-J Generalized Hausdorff Matrices Not of Type M Abstract ad Applied Aalysis Volume 2011, Article ID 527360, 5 pages doi:10.1155/2011/527360 Research Article Some E-J Geeralized Hausdorff Matrices Not of Type M T. Selmaogullari, 1 E. Savaş, 2 ad B. E.

More information

Modeling and Estimation of a Bivariate Pareto Distribution using the Principle of Maximum Entropy

Modeling and Estimation of a Bivariate Pareto Distribution using the Principle of Maximum Entropy Sri Laka Joural of Applied Statistics, Vol (5-3) Modelig ad Estimatio of a Bivariate Pareto Distributio usig the Priciple of Maximum Etropy Jagathath Krisha K.M. * Ecoomics Research Divisio, CSIR-Cetral

More information

Newton Homotopy Solution for Nonlinear Equations Using Maple14. Abstract

Newton Homotopy Solution for Nonlinear Equations Using Maple14. Abstract Joural of Sciece ad Techology ISSN 9-860 Vol. No. December 0 Newto Homotopy Solutio for Noliear Equatios Usig Maple Nor Haim Abd. Rahma, Arsmah Ibrahim, Mohd Idris Jayes Faculty of Computer ad Mathematical

More information

Numerical Method for Blasius Equation on an infinite Interval

Numerical Method for Blasius Equation on an infinite Interval Numerical Method for Blasius Equatio o a ifiite Iterval Alexader I. Zadori Omsk departmet of Sobolev Mathematics Istitute of Siberia Brach of Russia Academy of Scieces, Russia zadori@iitam.omsk.et.ru 1

More information

On Some Properties of Digital Roots

On Some Properties of Digital Roots Advaces i Pure Mathematics, 04, 4, 95-30 Published Olie Jue 04 i SciRes. http://www.scirp.org/joural/apm http://dx.doi.org/0.436/apm.04.46039 O Some Properties of Digital Roots Ilha M. Izmirli Departmet

More information

On the convergence, consistence and stability of a standard finite difference scheme

On the convergence, consistence and stability of a standard finite difference scheme AMERICAN JOURNAL OF SCIENTIFIC AND INDUSTRIAL RESEARCH 2, Sciece Huβ, ttp://www.sciub.org/ajsir ISSN: 253-649X, doi:.525/ajsir.2.2.2.74.78 O te covergece, cosistece ad stabilit of a stadard fiite differece

More information

Discrete Orthogonal Moment Features Using Chebyshev Polynomials

Discrete Orthogonal Moment Features Using Chebyshev Polynomials Discrete Orthogoal Momet Features Usig Chebyshev Polyomials R. Mukuda, 1 S.H.Og ad P.A. Lee 3 1 Faculty of Iformatio Sciece ad Techology, Multimedia Uiversity 75450 Malacca, Malaysia. Istitute of Mathematical

More information

-ORDER CONVERGENCE FOR FINDING SIMPLE ROOT OF A POLYNOMIAL EQUATION

-ORDER CONVERGENCE FOR FINDING SIMPLE ROOT OF A POLYNOMIAL EQUATION NEW NEWTON-TYPE METHOD WITH k -ORDER CONVERGENCE FOR FINDING SIMPLE ROOT OF A POLYNOMIAL EQUATION R. Thukral Padé Research Cetre, 39 Deaswood Hill, Leeds West Yorkshire, LS7 JS, ENGLAND ABSTRACT The objective

More information

Curve Sketching Handout #5 Topic Interpretation Rational Functions

Curve Sketching Handout #5 Topic Interpretation Rational Functions Curve Sketchig Hadout #5 Topic Iterpretatio Ratioal Fuctios A ratioal fuctio is a fuctio f that is a quotiet of two polyomials. I other words, p ( ) ( ) f is a ratioal fuctio if p ( ) ad q ( ) are polyomials

More information

A Pseudo Spline Methods for Solving an Initial Value Problem of Ordinary Differential Equation

A Pseudo Spline Methods for Solving an Initial Value Problem of Ordinary Differential Equation Joural of Matematics ad Statistics 4 (: 7-, 008 ISSN 549-3644 008 Sciece Publicatios A Pseudo Splie Metods for Solvig a Iitial Value Problem of Ordiary Differetial Equatio B.S. Ogudare ad G.E. Okeca Departmet

More information

A statistical method to determine sample size to estimate characteristic value of soil parameters

A statistical method to determine sample size to estimate characteristic value of soil parameters A statistical method to determie sample size to estimate characteristic value of soil parameters Y. Hojo, B. Setiawa 2 ad M. Suzuki 3 Abstract Sample size is a importat factor to be cosidered i determiig

More information

sin(n) + 2 cos(2n) n 3/2 3 sin(n) 2cos(2n) n 3/2 a n =

sin(n) + 2 cos(2n) n 3/2 3 sin(n) 2cos(2n) n 3/2 a n = 60. Ratio ad root tests 60.1. Absolutely coverget series. Defiitio 13. (Absolute covergece) A series a is called absolutely coverget if the series of absolute values a is coverget. The absolute covergece

More information

METHOD OF FUNDAMENTAL SOLUTIONS FOR HELMHOLTZ EIGENVALUE PROBLEMS IN ELLIPTICAL DOMAINS

METHOD OF FUNDAMENTAL SOLUTIONS FOR HELMHOLTZ EIGENVALUE PROBLEMS IN ELLIPTICAL DOMAINS Please cite this article as: Staisław Kula, Method of fudametal solutios for Helmholtz eigevalue problems i elliptical domais, Scietific Research of the Istitute of Mathematics ad Computer Sciece, 009,

More information

On Some Aspects of Random Walks for. Modelling Mobility in a Communication Network* E.R. Barnes

On Some Aspects of Random Walks for. Modelling Mobility in a Communication Network* E.R. Barnes ESL-P-783 Noveiber 1977 O Some Aspects of Radom Walks for Modellig Mobility i a Commuicatio Network* S.K. Leug-Ya-Cheog E.R. Bares This ote examies a two-dimesioal symmetric radom walk model of mobility

More information

Research Article A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences

Research Article A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences Discrete Dyamics i Nature ad Society Article ID 210761 4 pages http://dxdoiorg/101155/2014/210761 Research Article A Uified Weight Formula for Calculatig the Sample Variace from Weighted Successive Differeces

More information

Recurrence Relations

Recurrence Relations Recurrece Relatios Aalysis of recursive algorithms, such as: it factorial (it ) { if (==0) retur ; else retur ( * factorial(-)); } Let t be the umber of multiplicatios eeded to calculate factorial(). The

More information

Algorithm of Superposition of Boolean Functions Given with Truth Vectors

Algorithm of Superposition of Boolean Functions Given with Truth Vectors IJCSI Iteratioal Joural of Computer Sciece Issues, Vol 9, Issue 4, No, July ISSN (Olie: 694-84 wwwijcsiorg 9 Algorithm of Superpositio of Boolea Fuctios Give with Truth Vectors Aatoly Plotikov, Aleader

More information

ANTI-SYNCHRONIZING SLIDING CONTROLLER DESIGN FOR IDENTICAL PAN SYSTEMS

ANTI-SYNCHRONIZING SLIDING CONTROLLER DESIGN FOR IDENTICAL PAN SYSTEMS ANTI-SYNCHRONIZING SLIDING CONTROLLER DESIGN FOR IDENTICAL PAN SYSTEMS Sudarapadia Vaidyaatha Research ad Developmet Cetre, Vel Tech Dr. RR & Dr. SR Techical Uiversity Avadi, Cheai-600 062, Tamil Nadu,

More information

Some Dynamical Behaviours of a Two Dimensional Nonlinear Map

Some Dynamical Behaviours of a Two Dimensional Nonlinear Map Iteratioal Joural of Moder Egieerig Research (IJMER) Vol.2, Issue.6, Nov-Dec. 202 pp-4302-4306 ISSN: 2249-6645 Some Dyamical Behaviours of a Two Dimesioal Noliear Map Tarii Kumar Dutta, Debasish Bhattacharjee

More information

Poincaré Problem for Nonlinear Elliptic Equations of Second Order in Unbounded Domains

Poincaré Problem for Nonlinear Elliptic Equations of Second Order in Unbounded Domains Advaces i Pure Mathematics 23 3 72-77 http://dxdoiorg/4236/apm233a24 Published Olie Jauary 23 (http://wwwscirporg/oural/apm) Poicaré Problem for Noliear Elliptic Equatios of Secod Order i Ubouded Domais

More information

Research Article Approximate Riesz Algebra-Valued Derivations

Research Article Approximate Riesz Algebra-Valued Derivations Abstract ad Applied Aalysis Volume 2012, Article ID 240258, 5 pages doi:10.1155/2012/240258 Research Article Approximate Riesz Algebra-Valued Derivatios Faruk Polat Departmet of Mathematics, Faculty of

More information

Preponderantly increasing/decreasing data in regression analysis

Preponderantly increasing/decreasing data in regression analysis Croatia Operatioal Research Review 269 CRORR 7(2016), 269 276 Prepoderatly icreasig/decreasig data i regressio aalysis Darija Marković 1, 1 Departmet of Mathematics, J. J. Strossmayer Uiversity of Osijek,

More information

An Alternative Scaling Factor In Broyden s Class Methods for Unconstrained Optimization

An Alternative Scaling Factor In Broyden s Class Methods for Unconstrained Optimization Joural of Mathematics ad Statistics 6 (): 63-67, 00 ISSN 549-3644 00 Sciece Publicatios A Alterative Scalig Factor I Broyde s Class Methods for Ucostraied Optimizatio Muhammad Fauzi bi Embog, Mustafa bi

More information

On the Variations of Some Well Known Fixed Point Theorem in Metric Spaces

On the Variations of Some Well Known Fixed Point Theorem in Metric Spaces Turkish Joural of Aalysis ad Number Theory, 205, Vol 3, No 2, 70-74 Available olie at http://pubssciepubcom/tjat/3/2/7 Sciece ad Educatio Publishig DOI:0269/tjat-3-2-7 O the Variatios of Some Well Kow

More information

Research Article Powers of Complex Persymmetric Antitridiagonal Matrices with Constant Antidiagonals

Research Article Powers of Complex Persymmetric Antitridiagonal Matrices with Constant Antidiagonals Hidawi Publishig orporatio ISRN omputatioal Mathematics, Article ID 4570, 5 pages http://dx.doi.org/0.55/04/4570 Research Article Powers of omplex Persymmetric Atitridiagoal Matrices with ostat Atidiagoals

More information

Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods

Solving a Nonlinear Equation Using a New Two-Step Derivative Free Iterative Methods Applied ad Computatioal Mathematics 07; 6(6): 38-4 http://www.sciecepublishiggroup.com/j/acm doi: 0.648/j.acm.070606. ISSN: 38-5605 (Prit); ISSN: 38-563 (Olie) Solvig a Noliear Equatio Usig a New Two-Step

More information

A comparative study of a system of Lotka-Voltera type of PDEs through perturbation methods

A comparative study of a system of Lotka-Voltera type of PDEs through perturbation methods Computatioal Ecology ad Software, 13, 3(4): 11-15 Article A comparative study of a system of Lotka-Voltera type of PDEs through perturbatio methods H. A. Wahab 1, M. Shakil 1, T. Kha 1, S. Bhatti, M. Naeem

More information

k-generalized FIBONACCI NUMBERS CLOSE TO THE FORM 2 a + 3 b + 5 c 1. Introduction

k-generalized FIBONACCI NUMBERS CLOSE TO THE FORM 2 a + 3 b + 5 c 1. Introduction Acta Math. Uiv. Comeiaae Vol. LXXXVI, 2 (2017), pp. 279 286 279 k-generalized FIBONACCI NUMBERS CLOSE TO THE FORM 2 a + 3 b + 5 c N. IRMAK ad M. ALP Abstract. The k-geeralized Fiboacci sequece { F (k)

More information