A Taylor Series Based Method for Solving a Two-dimensional Second-order Equation
|
|
- Leon Shepherd
- 5 years ago
- Views:
Transcription
1 Applied Mathematical Scieces, Vol. 8, 2014, o. 66, HIKARI Ltd, A Taylor Series Based Method for Solvig a Two-dimesioal Secod-order Equatio Samaeh Afshar Departmet of Mathematics, Islamic Azad Uiversity Cetral Tehra Brach, Tehra, Ira Copyright c 2014 Samaeh Afshar. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. Abstract I this paper, we focus o the two-dimesioal liear Telegraph equatio with some iitial ad boudary coditios. We trasform the model of partial differetial equatio (PDE) ito a system of first order, liear, ordiary differetial equatios (ODEs). Our method is based o fidig a solutio i the form of a polyomial i three variables U (x, y, t) = i=0 k=0 U(i, j, k)xi y j t k with udetermied coefficiets U(i, j, k). The mai idea of our process is based o the differetial trasformatio method (DTM). Keywords: Liear hyperbolic equatio; two-dimesioal Telegraph equatio; Differetial Trasformatio method 1 Itroductio I this paper we focus o the followig diffusio equatio i two space variables 2 u t +2α u 2 t + β2 u = δ 2 u x + γ 2 u + f(x, y, t), 0 <x<1, 0 <y<1, t>0, 2 y2 (1) while the iitial ad boudary coditios are u(x, y, 0) = p(x, y), u(x,y,0) = m(x, y),u(0,y,t)=q(y, t),u(x, 0,t)=h(x, t), t u(1,y,t)=r(y, t),u(x, 1,t)=g(x, t), 0 t T, 0 x 1, (2)
2 3256 Samaeh Afshar The fuctios f(x, y, t), p(x, y), q(y, t),h(x, t), r(y, t), g(x, t) ad m(x, y) are kow fuctios ad the costats α, β, δ ad γ are kow costats. For α>0, β = 0 ad δ = γ = 1, Eq. (1) represets a damped wave equatio ad for α > β > 0 ad δ = γ = 1, is called telegraph equatio. Dig ad Zhag[9], preseted a three level compact differece scheme of O(τ 4 + h 4 ) for the differece solutio of problem (1) ad (2). A efficiet approach for solvig the two dimesioal liear hyperbolic telegraph equatio by the compact fiite differece approximatio of fourth order ad the collocatio method have bee developed i [18]. Authors of [10, 11, 12] also studied Eq. (1) with other methods. For solvig these kids of equatios there are several methods, such as differetial trasformatio method [2, 3, 6, 4, 12, 11, 7, 8, 10, 21, 22, 23, 24, 25], Tau method [19, 20] ad homotopy perturbatio method [13]. A ew matrix formulatio techique with arbitrary polyomial bases has bee proposed for the umerical/aalytical solutio of the heat equatio with olocal boudary coditio [1] ad Two matrix formulatio techiques based o the shifted stadard ad shifted Chebyshev bases are proposed for the umerical solutio of the wave equatio with the o-local boudary coditio [5]. 2 Three-dimesioal differetial trasform Cosider a fuctio of two variables w(x, y, t), ad suppose that it ca be represeted as a product of two sigle-variable fuctios, i.e., w(x, y, t) = ϕ(x)φ(y)ψ(t). The the fuctio w(x, y, t) ca be represeted as w(x, y, t) = W (i, j, k)x i y j t k. (3) i=0 k=0 where W (i, j, k) is called the spectrum of w(x, y, t). Now we itroduce the basic defiitios ad operatios of three-dimesioal DT as follows[8]. Defiitio 2.1. Give a w fuctio which has three compoets such as x, y, t. Three-dimesioal differetial trasform of w(x, y, t) is defied [ ] W (i, j, k) = 1 i+j+k w(x, y, t), i!j!k! x i y j t (4) k x=x 0,y=y 0,t=t 0 where the spectrum fuctio W (i, j, k) is the trasformed fuctio, which is also called the T-fuctio. let w(x, y, t) as the origial fuctio while the uppercase W (i, j, k) stads for the trasformed fuctio. Now we defie The
3 A Taylor series based method 3257 differetial iverse trasform of W (i, j, k) as followig: w(x, y, t) = W (i, j, k)(x x 0 ) i (y y 0 ) j (t t 0 ) k. (5) i=0 k=0 Usig Eq. (4) i (5), we have w(x, y, t) = i=0 k=0 1 i!j!k! = i=0 k=0 W (i, j, k)xi y j t k. [ ] i+j+k w(x, t) x i y j t k x i y j t k x=x 0,y=y 0,t=t 0 Now we give the fudametal theorems for the three-dimesioal case of DTM by usig the followig theorem Theorem 2.1. Assume that W (i, j, k), U(i, j, k) ad V (i, j, k) are the differetial trasforms of the fuctios w(x, y, t), u(x, y, t) ad v(x, y, t), respectively; the: 1 If w(x, y, t) =u(x, y, t)±v(x, y, t), the W (i, j, k) =U(i, j, k)±v (i, j, k), 2 If w(x, y, t) =cu(x, y, t), where c R, the W (i, j, k) =cu(i, j, k) 3 If w(x, y, t) = u(x, y, t), the W (i, j, k) =(k +1)U(i, j, k +1) t 4 If w(x, y, t) = r+s+m u(x, y, t), the x r y s t m W (i, j, k) = (i+r)!(j+s)!(k+m)! U(i + r, j + s, k + m) i!j!k! Proof. See [8]. 3 Reformulatio of the problem I this sectio, we covert the problem (1) ad (2) ito a system of first order, liear, ordiary differetial equatio. I Eqs. (1) ad (2), the fuctios f(x, y, t), p(x, y), g(x, y), h(x, t), r(y, t) ad m(t) geerally are ot polyomials. We assume that these fuctios are polyomial or they ca be approximated by polyomials to ay degree of accuracy. The if we suppose that f(x, y, t) i=0 k=0 F (i, j, k)xi y j t k,p(x, y) i=0 P (i, j)xi y j, g(x, y) i=0 G(i, j)xi y j,h(x, t) i=0 k=0 H(i, k)xi t k, r(y, t) k=0 R(i, k)yj t k,m(x, y) i=0 M(i, j)xi y j, (7) Therefore we cosider approximate solutio of the form (6) U (x, y, t) = U(i, j, k)x i y j t k, (8) i=0 k=0
4 3258 Samaeh Afshar where U (x, y, t) is the approximatio of u(x, y, t). If we fid the values of U(i, j, k), for i, j, k =0, 1, 2,...,, the U (x, y, t) ca be foud by usig Eq. (7). To fid these ukows, we proceed as follows. By utilizig Theorem 2.1 ad Eqs. (7),(8) ito Eqs. (1) ad (2), we get (k + 1)(k +2)U(i, j, k +2)+α(k +1)U(i, j, k +1)+βU(i, j, k) =δ(i + 1)(i +2) U(i +2,j,k)+γ(j + 1)(j +2)U(i, j +2,k)+F (i, j, k) i, j, k =0, 1, 2,...,. i=0 U(i, j, 0)xi y j = i=0 P (i, j)xi y j,i,, 1,...,. k=0 U(0,j,k)yj t k = k=0 Q(j, k)yj t k,j,k=0, 1,...,. i=0 k=0 U(i, 0,k)xi t k = i=0 k=0 H(i, k)xi t k, i,k =0, 1,...,. i=0 k=0 U(i, j, k)yj t k = k=0 R(j, k)yj t k,j,k=0, 1,...,. i=0 k=0 U(i, j, k)xi t k = i=0 k=0 G(i, k)xi t k,i,k=0, 1,...,. i=0 U(i, j, 1)xi y j = M(i, j), i,j =0, 1,...,. (9) Therefore, to fidig the values of U(i, j, k), for i, j, k =0, 1, 2,...,, we must costruct a system of ( + 1)( + 1)( + 1) equatios. To this ed we arrage the obtaied liear equatios from the previous sectio. Because the problems (1) ad (2) have bee ot defied for etire of the rage, we select oly the equatios that satisfy i the defied rage. Firstly, the ( +1) 2 values of U ca be obtaied from as follows: U(i, j, 0) = P (i, j), i,, 1,...,. U(0,j,k)=Q(j, k), j =0, 1,...,, k =1, 2,...,. U(i, 0,k)=H(i, k), i,k=1, 2,...,. U(i, j, 1) = M(i, j), i,j =0, 1,...,. (10) So, we ca obtai values of U idepedetly. The the remaider values of U must be obtaied from the other equatios. We choose equatios from he followig equatios i=0 U(i, j, k) =R(j, k), j =1,..., 1, k=2,..., 1, i=0 U(i, 1,k)=R(1,k), i=0 U(i,, k) =R(, k),k =2,..., 1, i=0 U(i, j, ) =R(j, ),j =2,..., 1, U(i, j, k) =G(i, k), i=1,..., 1, k=2,..., 1, U(1,j,k)=G(1,k), U(, j, k) =G(, k), k=2,..., 1, U(i, j, ) =G(i, ), i=2,..., 2, (11)
5 A Taylor series based method 3259 Fially, the remaider equatios ca be foud i the form of (k + 1)(k +2)U(i, j, k +2)+α(k +1)U(i, j, k +1)+βU(i, j, k) = δ(i + 1)(i +2)U(i +2,j,k)+γ(j + 1)(j +2)U(i, j +2,k) +F (i, j, k), i,j =1, 2,..., 2, k=0, 1,..., 2, (k + 1)(k +2)U(0,j,k+2)+α(k +1)U(0,j,k+1)+βU(0,j,k) =2δU(2,j,k)+γ(j + 1)(j +2)U(0,j+2,k) +F (0,j,k), j =1, 2,..., 2, k=2,..., 2 (k + 1)(k +2)U(i, 0,k+2)+α(k +1)U(i, 0,k+1)+βU(i, 0,k) = δ(i + 1)(i +2)U(i +2, 0,k)+2γU(i, 2,k) +F (i, 0,k), i =1, 2,...,, k =2,..., 2. (12) Eqs. (10)-(12) give a liear algebraic system of equatios that by solvig this system, the remaider values of U will be obtaied ad the from Eq. (13), we ca obtaie U (x, y, t) that it is the approximatio of u(x, y, t). 4 Coclusios I this article, the solutio of the secod order two space dimesioal hyperbolic telegraph equatio has bee discussed by usig differetial trasformatio method. Covertig the model of PDE to a system of liear equatios, is the mai part of this paper. The computatioal difficulties of the other methods ca be reduced by applyig this process. Refereces [1] B. Soltaalizadeh, Numerical aalysis of the oe-dimesioal Heat equatio subject to a boudary itegral specificatio, Optics Commuicatios, 284 (2011), [2] B. Soltaalizadeh, A. Yildirim, Applicatio of Differetial Trasformatio method for umerical computatio of Regularized Log Wave equatio, Z. fuer Naturforschug A., 67a (2012), [3] B. Soltaalizadeh, Applicatio of Differetial Trasformatio Method for Numerical Aalysis of Kawahara Equatio, Australia Joural of Basic ad Applied Scieces, 5(12) (2011), [4] B. Soltaalizadeh, Applicatio of Differetial Trasformatio method for solvig a fourth-order parabolic partial differetial equatios, Iteratioal joural of pure ad applied mathematics, 78 (3) (2012),
6 3260 Samaeh Afshar [5] H.R. Ghehsareh, B. Soltaalizadeh,S. Abbasbady, A matrix formulatio to the wave equatio with olocal boudary coditio, Iter. J. Comput. Math., 88 (2011), [6] B. Soltaalizadeh, Differetial Trasformatio method for solvig oespace-dimesioal Telegraph equatio, computatioal applied mathematics, 30(3) (2011), [7] B. Soltaalizadeh, M. Zarebia, Numerical aalysis of the liear ad oliear Kuramoto-Sivashisky equatio by usig Differetial Trasformatio method, Iter. J. Appl. Math. Mechaics, 7(12) (2011), [8] F. Ayaz, Solutios of the systems of differetial equatios by differetial trasform method, Appl. Math. Comput., 147 (2004), [9] H. Dig, Y. Zhag.A ew fourth order compact fiite differece scheme for the two-dimesioal secod-order hyperbolic equatio. J. Comput. Appl. Math., 230 (2009), [10] D. Degab, C. Zhaga, Applicatio of a fourth-order compact ADI method to solve a two-dimesioal liear hyperbolic equatio 90 (2013), [11] B. Pekme, M. Tezer-Sezgi, Differetial Quadrature Solutio of Hyperbolic Telegraph Equatio, doi: /2012/ [12] A. Mohebbi ad M. Dehgha, High order compact solutio of the oespace-dimesioal liear hyperbolic equatio, Numerical Methods for Partial Differetial Equatios, 24 (2008), [13] S.T.Mohyud-Di, A.Yildirim, G.Demirli, Travelig wave solutios of Whitham-Broer-Kaup equatios by homotopy perturbatio method, Joural of Kig Saud Uiversity-Sciece, 22 (2010), [14] A. Shabai Shahrbabaki, R. Abazari, Perturbatio method for heat exchage betwee a gas ad solid particles, J. appl. Mech. Tech. Phys, 50(6) (2009), [15] RK. Mohaty, MK. Jai, A ucoditioally stable alteratig directio implicit scheme for the two-space dimesioal liear hyperbolic equatio, Numer Meth Partial Diff Eq. 7 (2001), [16] RK. Mohaty, RK. Jaix, U. Arora, A ucoditioally stable ADI method for the liear hyperbolic equatio i three space dimesioal, It. J. Comput. Math., 79 (2002),
7 A Taylor series based method 3261 [17] M. Dehgha,A. Shokri, A meshless method for umerical solutio of a liear hyperbolic equatio with variable coefficiets i two space dimesios, Numer Meth Partial Diff Eq., 25 (2009), [18] M. Dehgha, A. Mohebbi, High order implicit collocatio method for the solutio of two-dimesioal liear hyperbolic equatio, Numer. Meth. Partial Diff. Eq., 25 (2009), [19] B. Soltaalizadeh, H.R. Ghehsareh, S. Abbasbady, Developmet of the tau method for the umerical study of a fourth-order parabolic partial differetial equatio, U.P.B. Sci. Bull., Series A, 75 (2013), [20] B. Soltaalizadeh, H.R. Ghehsareh, S. Abbasbady, A super accurate Shifted Tau method for umerical computatio of the Sobolev-type differetial equatio with olocal boudary coditios, Applied Mathematics ad Computatio, 236 (2014), [21] B. Babayar, B. Soltaalizadeh, Numerical solutio for system of sigular oliear volterra itegro-differetial equatios by Newto-Product method, Applied mathematics ad computatio, 219 (2013), [22] B. Babayar, B. Soltaalizadeh, Numerical solutio of oliear sigular Volterra itegral system by the Newto-Product itegratio method, Mathematical ad computer modellig, 58 (2013), [23] B. Soltaalizadeh, HR Ghehsareh, A. Yildirm, S. Abbasbady, O the Aalytic Solutio for a Steady Magetohydrodyamic Equatio, Zeitschrift fuer Naturforschug A., 68a (2013), [24] H. Roohai Ghehsareh, S. Abbasbady, B. Soltaalizadeh, Aalytical solutios of the slip MHD viscous flow over a stretchig sheet by usig the Laplace Adomia Decompositio Method, Zeitschrift fuer Naturforschug A., 67a, (2012), [25] S. Shahmorad, A. Borhaifar, B. Soltaalizadeh, A matrix formulatio of the heat equatio with olocal boudary coditios, Computatioal Methods i Applied Mathematics, 12 (2012), Received: May 1, 2014
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 informationSolution of Differential Equation from the Transform Technique
Iteratioal Joural of Computatioal Sciece ad Mathematics ISSN 0974-3189 Volume 3, Number 1 (2011), pp 121-125 Iteratioal Research Publicatio House http://wwwirphousecom Solutio of Differetial Equatio from
More informationComparison 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 informationResearch 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 informationTaylor 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 informationExact 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 informationSimilarity 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 informationNUMERICAL METHOD FOR SINGULARLY PERTURBED DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS
THERMAL SCIENCE, Year 07, Vol., No. 4, pp. 595-599 595 NUMERICAL METHOD FOR SINGULARLY PERTURBED DELAY PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS by Yula WANG *, Da TIAN, ad Zhiyua LI Departmet of Mathematics,
More informationDECOMPOSITION 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 informationNumerical Solution of the Two Point Boundary Value Problems By Using Wavelet Bases of Hermite Cubic Spline Wavelets
Australia Joural of Basic ad Applied Scieces, 5(): 98-5, ISSN 99-878 Numerical Solutio of the Two Poit Boudary Value Problems By Usig Wavelet Bases of Hermite Cubic Splie Wavelets Mehdi Yousefi, Hesam-Aldie
More informationA 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 informationNewton 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 informationResearch Article Laplace Transform Collocation Method for Solving Hyperbolic Telegraph Equation
Hidawi Iteratioal Joural of Egieerig Mathematics Volume 7, Article ID 596, 9 pages https://doi.org/.55/7/596 Research Article Laplace Trasform Collocatio Method for Solvig Hyperbolic Telegraph Equatio
More informationA 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 informationHigher-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 informationA 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 informationNumerical 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 informationResearch Article Numerical Solution of Fractional Integro-Differential Equations by Least Squares Method and Shifted Chebyshev Polynomial
Mathematical Problems i Egieerig Volume 24, Article ID 43965, 5 pages http://dx.doi.org/.55/24/43965 Research Article Numerical Solutio of Fractioal Itegro-Differetial Equatios by Least Squares Method
More informationPAijpam.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 informationSome 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 informationwavelet collocation method for solving integro-differential equation.
IOSR Joural of Egieerig (IOSRJEN) ISSN (e): 5-3, ISSN (p): 78-879 Vol. 5, Issue 3 (arch. 5), V3 PP -7 www.iosrje.org wavelet collocatio method for solvig itegro-differetial equatio. Asmaa Abdalelah Abdalrehma
More informationA 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 informationPOWER SERIES SOLUTION OF FIRST ORDER MATRIX DIFFERENTIAL EQUATIONS
Joural of Applied Mathematics ad Computatioal Mechaics 4 3(3) 3-8 POWER SERIES SOLUION OF FIRS ORDER MARIX DIFFERENIAL EQUAIONS Staisław Kukla Izabela Zamorska Istitute of Mathematics Czestochowa Uiversity
More informationNumerical 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 informationMonte Carlo Optimization to Solve a Two-Dimensional Inverse Heat Conduction Problem
Australia Joural of Basic Applied Scieces, 5(): 097-05, 0 ISSN 99-878 Mote Carlo Optimizatio to Solve a Two-Dimesioal Iverse Heat Coductio Problem M Ebrahimi Departmet of Mathematics, Karaj Brach, Islamic
More informationarxiv: v1 [cs.sc] 2 Jan 2018
Computig the Iverse Melli Trasform of Holoomic Sequeces usig Kovacic s Algorithm arxiv:8.9v [cs.sc] 2 Ja 28 Research Istitute for Symbolic Computatio RISC) Johaes Kepler Uiversity Liz, Alteberger Straße
More informationLOWER BOUNDS FOR THE BLOW-UP TIME OF NONLINEAR PARABOLIC PROBLEMS WITH ROBIN BOUNDARY CONDITIONS
Electroic Joural of Differetial Equatios, Vol. 214 214), No. 113, pp. 1 5. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.ut.edu ftp ejde.math.txstate.edu LOWER BOUNDS FOR THE BLOW-UP
More informationApplication of Homotopy Analysis Method for Solving various types of Problems of Ordinary Differential Equations
Iteratioal Joural o Recet ad Iovatio Treds i Coputig ad Couicatio IN: 31-8169 Volue: 5 Issue: 5 16 Applicatio of Hootopy Aalysis Meod for olvig various types of Probles of Ordiary Differetial Equatios
More informationEXACT SOLUTION OF WHITHAM-BROER-KAUP SHALLOW WATER WAVE EQUATIONS
Joural of Sciece ad Arts Year 5, No. (3), pp. 5-, 5 ORIGINAL PAPER EXACT SOLUTION OF WHITHAM-BROER-KAUP SHALLOW WATER WAVE EQUATIONS JAMSHAD AHMAD, MARIYAM MUSHTAQ, NADEEM SAJJAD 3 Mauscript received:
More informationNTMSCI 5, No. 1, (2017) 26
NTMSCI 5, No. 1, - (17) New Treds i Mathematical Scieces http://dx.doi.org/1.85/tmsci.17.1 The geeralized successive approximatio ad Padé approximats method for solvig a elasticity problem of based o the
More informationResearch 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 informationThe Numerical Solution of Singular Fredholm Integral Equations of the Second Kind
WDS' Proceedigs of Cotributed Papers, Part I, 57 64, 2. ISBN 978-8-7378-39-2 MATFYZPRESS The Numerical Solutio of Sigular Fredholm Itegral Equatios of the Secod Kid J. Rak Charles Uiversity, Faculty of
More informationNew Inequalities of Hermite-Hadamard-like Type for Functions whose Second Derivatives in Absolute Value are Convex
It. Joural of Math. Aalysis, Vol. 8, 1, o. 16, 777-791 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.1988/ijma.1.1 New Ieualities of Hermite-Hadamard-like Type for Fuctios whose Secod Derivatives i
More informationChapter 10: Power Series
Chapter : Power Series 57 Chapter Overview: Power Series The reaso series are part of a Calculus course is that there are fuctios which caot be itegrated. All power series, though, ca be itegrated because
More informationThe 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 informationTHE TRANSFORMATION MATRIX OF CHEBYSHEV IV BERNSTEIN POLYNOMIAL BASES
Joural of Mathematical Aalysis ISSN: 17-341, URL: http://iliriascom/ma Volume 7 Issue 4(16, Pages 13-19 THE TRANSFORMATION MATRIX OF CHEBYSHEV IV BERNSTEIN POLYNOMIAL BASES ABEDALLAH RABABAH, AYMAN AL
More informationNumerical solution of Bagley-Torvik equation using Chebyshev wavelet operational matrix of fractional derivative
It. J. Adv. Appl. Math. ad Mech. () (04) 83-9 ISSN: 347-59 Available olie at www.iaamm.com Iteratioal Joural of Advaces i Applied Mathematics ad Mechaics Numerical solutio of Bagley-Torvik equatio usig
More informationμ 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 informationExact Solutions of the Generalized Benjamin Equation and (3 + 1)- Dimensional Gkp Equation by the Extended Tanh Method
Available at http://pvamuedu/aam Appl Appl Math ISSN: 93-9466 Vol 7, Issue (Jue 0), pp 75 87 Applicatios ad Applied Mathematics: A Iteratioal Joural (AAM) Exact Solutios of the Geeralized Bejami Equatio
More informationResearch 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 informationThe 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 informationReconstruction of the Volterra-type integro-differential operator from nodal points
Keski Boudary Value Problems 18 18:47 https://doi.org/1.1186/s13661-18-968- R E S E A R C H Ope Access Recostructio of the Volterra-type itegro-differetial operator from odal poits Baki Keski * * Correspodece:
More informationCOMPLEX FACTORIZATIONS OF THE GENERALIZED FIBONACCI SEQUENCES {q n } Sang Pyo Jun
Korea J. Math. 23 2015) No. 3 pp. 371 377 http://dx.doi.org/10.11568/kjm.2015.23.3.371 COMPLEX FACTORIZATIONS OF THE GENERALIZED FIBONACCI SEQUENCES {q } Sag Pyo Ju Abstract. I this ote we cosider a geeralized
More informationDETERMINATION OF MECHANICAL PROPERTIES OF A NON- UNIFORM BEAM USING THE MEASUREMENT OF THE EXCITED LONGITUDINAL ELASTIC VIBRATIONS.
ICSV4 Cairs Australia 9- July 7 DTRMINATION OF MCHANICAL PROPRTIS OF A NON- UNIFORM BAM USING TH MASURMNT OF TH XCITD LONGITUDINAL LASTIC VIBRATIONS Pavel Aokhi ad Vladimir Gordo Departmet of the mathematics
More informationNumerical Conformal Mapping via a Fredholm Integral Equation using Fourier Method ABSTRACT INTRODUCTION
alaysia Joural of athematical Scieces 3(1): 83-93 (9) umerical Coformal appig via a Fredholm Itegral Equatio usig Fourier ethod 1 Ali Hassa ohamed urid ad Teh Yua Yig 1, Departmet of athematics, Faculty
More informationTHE NUMERICAL SOLUTION OF THE NEWTONIAN FLUIDS FLOW DUE TO A STRETCHING CYLINDER BY SOR ITERATIVE PROCEDURE ABSTRACT
Europea Joural of Egieerig ad Techology Vol. 3 No., 5 ISSN 56-586 THE NUMERICAL SOLUTION OF THE NEWTONIAN FLUIDS FLOW DUE TO A STRETCHING CYLINDER BY SOR ITERATIVE PROCEDURE Atif Nazir, Tahir Mahmood ad
More informationLøsningsførslag i 4M
Norges tekisk aturviteskapelige uiversitet Istitutt for matematiske fag Side 1 av 6 Løsigsførslag i 4M Oppgave 1 a) A sketch of the graph of the give f o the iterval [ 3, 3) is as follows: The Fourier
More informationA numerical Technique Finite Volume Method for Solving Diffusion 2D Problem
The Iteratioal Joural Of Egieerig d Sciece (IJES) Volume 4 Issue 10 Pages PP -35-41 2015 ISSN (e): 2319 1813 ISSN (p): 2319 1805 umerical Techique Fiite Volume Method for Solvig Diffusio 2D Problem 1 Mohammed
More informationx x x 2x x N ( ) p NUMERICAL METHODS UNIT-I-SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS By Newton-Raphson formula
NUMERICAL METHODS UNIT-I-SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS. If g( is cotiuous i [a,b], te uder wat coditio te iterative (or iteratio metod = g( as a uique solutio i [a,b]? '( i [a,b].. Wat
More informationSome 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 informationReview Article Incomplete Bivariate Fibonacci and Lucas p-polynomials
Discrete Dyamics i Nature ad Society Volume 2012, Article ID 840345, 11 pages doi:10.1155/2012/840345 Review Article Icomplete Bivariate Fiboacci ad Lucas p-polyomials Dursu Tasci, 1 Mirac Ceti Firegiz,
More informationHOMOTOPY PERTURBATION METHOD FOR VISCOUS HEATING IN PLANE COUETTE FLOW
Yu, Y.-S. et al.: Homotopy Perturbatio Method for Viscous Heatig THERMAL SCIENCE, Year 13, Vol. 17, No. 5, pp. 1355-136 1355 HOMOTOPY PERTURBATION METHOD FOR VISCOUS HEATING IN PLANE COUETTE FLOW by Yi-Sha
More information-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 informationApplication 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 informationFUZZY ALTERNATING DIRECTION IMPLICIT METHOD FOR SOLVING PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS IN THREE DIMENSIONS
FUZZY ALTERNATING DIRECTION IMPLICIT METHOD FOR SOLVING PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS IN THREE DIMENSIONS N.Mugutha *1, B.Jessaili Jeba #2 *1 Assistat Professor, Departmet of Mathematics, M.V.Muthiah
More informationWe are mainly going to be concerned with power series in x, such as. (x)} converges - that is, lims N n
Review of Power Series, Power Series Solutios A power series i x - a is a ifiite series of the form c (x a) =c +c (x a)+(x a) +... We also call this a power series cetered at a. Ex. (x+) is cetered at
More informationSolving 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 informationChapter 4 : Laplace Transform
4. Itroductio Laplace trasform is a alterative to solve the differetial equatio by the complex frequecy domai ( s = σ + jω), istead of the usual time domai. The DE ca be easily trasformed ito a algebraic
More informationTMA4205 Numerical Linear Algebra. The Poisson problem in R 2 : diagonalization methods
TMA4205 Numerical Liear Algebra The Poisso problem i R 2 : diagoalizatio methods September 3, 2007 c Eiar M Røquist Departmet of Mathematical Scieces NTNU, N-749 Trodheim, Norway All rights reserved A
More informationA) is empty. B) is a finite set. C) can be a countably infinite set. D) can be an uncountable set.
M.A./M.Sc. (Mathematics) Etrace Examiatio 016-17 Max Time: hours Max Marks: 150 Istructios: There are 50 questios. Every questio has four choices of which exactly oe is correct. For correct aswer, 3 marks
More informationBoundary layer problem on conveyor belt. Gabriella Bognár University of Miskolc 3515 Miskolc-Egyetemváros, Hungary
Boudary layer problem o coveyor belt Gabriella Bogár Uiversity of Miskolc 355 Miskolc-Egyetemváros, Hugary e-mail: matvbg@ui-miskolc.hu Abstract: A techologically importat source of the boudary layer pheomeo
More informationPC5215 Numerical Recipes with Applications - Review Problems
PC55 Numerical Recipes with Applicatios - Review Problems Give the IEEE 754 sigle precisio bit patter (biary or he format) of the followig umbers: 0 0 05 00 0 00 Note that it has 8 bits for the epoet,
More informationIntroduction to Optimization Techniques. How to Solve Equations
Itroductio to Optimizatio Techiques How to Solve Equatios Iterative Methods of Optimizatio Iterative methods of optimizatio Solutio of the oliear equatios resultig form a optimizatio problem is usually
More informationCHAPTER 5. Theory and Solution Using Matrix Techniques
A SERIES OF CLASS NOTES FOR 2005-2006 TO INTRODUCE LINEAR AND NONLINEAR PROBLEMS TO ENGINEERS, SCIENTISTS, AND APPLIED MATHEMATICIANS DE CLASS NOTES 3 A COLLECTION OF HANDOUTS ON SYSTEMS OF ORDINARY DIFFERENTIAL
More informationResearch 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 informationConvergence of Random SP Iterative Scheme
Applied Mathematical Scieces, Vol. 7, 2013, o. 46, 2283-2293 HIKARI Ltd, www.m-hikari.com Covergece of Radom SP Iterative Scheme 1 Reu Chugh, 2 Satish Narwal ad 3 Vivek Kumar 1,2,3 Departmet of Mathematics,
More informationHALF-SWEEP GAUSS-SEIDEL ITERATION APPLIED TO TIME-FRACTIONAL DIFFUSION EQUATIONS
Jural Karya Asli Loreka Ahli Matematik Vol. 8 No. () Page 06-0 Jural Karya Asli Loreka Ahli Matematik HALF-SWEEP GAUSS-SEIDEL ITERATION APPLIED TO TIME-FRACTIONAL DIFFUSION EQUATIONS A. Suarto J. Sulaima
More informationRadial Basis Function-Pseudospectral Method for Solving Non-Linear Whitham-Broer-Kaup Model
Sohag J. Math. 4 No. 1 13-18 017 13 Sohag Joural of Mathematics A Iteratioal Joural http://dx.doi.org/10.18576/sjm/040103 Radial Basis Fuctio-Pseudospectral Method for Solvig No-Liear Whitham-Broer-Kaup
More informationResearch 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 informationADM Solution of Flow Field and Convective Heat Transfer over a Parallel Flat Plate and Comparison with the Forth Order Runge Kutta Method
Australia Joural of Basic ad Applied Scieces, 5(: -8, ISSN 99-878 ADM Solutio of Flow Field ad Covective Heat Trasfer over a Parallel Flat Plate ad Compariso with the Forth Order Ruge Kutta Method Arma
More informationInverse Nodal Problems for Differential Equation on the Half-line
Australia Joural of Basic ad Applied Scieces, 3(4): 4498-4502, 2009 ISSN 1991-8178 Iverse Nodal Problems for Differetial Equatio o the Half-lie 1 2 3 A. Dabbaghia, A. Nematy ad Sh. Akbarpoor 1 Islamic
More informationZ - 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 informationAN INVERSE STURM-LIOUVILLE PROBLEM WITH A GENERALIZED SYMMETRIC POTENTIAL
Electroic Joural of Differetial Equatios, Vol. 7 (7, No. 4, pp. 7. ISSN: 7-669. URL: http://ejde.math.txstate.edu or http://ejde.math.ut.edu AN INVERSE STURM-LIOUVILLE PROBLEM WITH A GENERALIZED SYMMETRIC
More informationStreamfunction-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 informationAn Iterative Method for Solving Unsymmetric System of Fuzzy Linear Equations
The SIJ Trasactios o Computer Sciece Egieerig & its Applicatios (CSEA) Vol. No. 5 November-December 03 A Iterative Method for Solvig Usymmetric System of Fuzzy Liear Equatios Majid Hasazadeh* & Hossei
More informationFind quadratic function which pass through the following points (0,1),(1,1),(2, 3)... 11
Adrew Powuk - http://www.powuk.com- Math 49 (Numerical Aalysis) Iterpolatio... 4. Polyomial iterpolatio (system of equatio)... 4.. Lier iterpolatio... 5... Fid a lie which pass through (,) (,)... 8...
More information: Transforms and Partial Differential Equations
Trasforms ad Partial Differetial Equatios 018 SUBJECT NAME : Trasforms ad Partial Differetial Equatios SUBJECT CODE : MA 6351 MATERIAL NAME : Part A questios REGULATION : R013 WEBSITE : wwwharigaeshcom
More informationFinite 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 informationAnalytical 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 informationChapter 9: Numerical Differentiation
178 Chapter 9: Numerical Differetiatio Numerical Differetiatio Formulatio of equatios for physical problems ofte ivolve derivatives (rate-of-chage quatities, such as velocity ad acceleratio). Numerical
More informationA GENERALIZED CHEBYSHEV FINITE DIFFERENCE METHOD FOR HIGHER ORDER BOUNDARY VALUE PROBLEMS
A GEERALIZED CHEBYSHEV FIITE DIFFERECE METHOD FOR HIGHER ORDER BOUDARY VALUE PROBLEMS Soer Aydilik Departmet of Mathematics, Faculty of Arts ad Scieces, Isik Uiversity, 34980, Istabul, Turkey Ahmet Kiris
More informationLecture 8: Solving the Heat, Laplace and Wave equations using finite difference methods
Itroductory lecture otes o Partial Differetial Equatios - c Athoy Peirce. Not to be copied, used, or revised without explicit writte permissio from the copyright ower. 1 Lecture 8: Solvig the Heat, Laplace
More informationTaylor expansion: Show that the TE of f(x)= sin(x) around. sin(x) = x - + 3! 5! L 7 & 8: MHD/ZAH
Taylor epasio: Let ƒ() be a ifiitely differetiable real fuctio. A ay poit i the eighbourhood of 0, the fuctio ƒ() ca be represeted by a power series of the followig form: X 0 f(a) f() f() ( ) f( ) ( )
More informationSession 5. (1) Principal component analysis and Karhunen-Loève transformation
200 Autum semester Patter Iformatio Processig Topic 2 Image compressio by orthogoal trasformatio Sessio 5 () Pricipal compoet aalysis ad Karhue-Loève trasformatio Topic 2 of this course explais the image
More informationOn Generalized Fibonacci Numbers
Applied Mathematical Scieces, Vol. 9, 215, o. 73, 3611-3622 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.12988/ams.215.5299 O Geeralized Fiboacci Numbers Jerico B. Bacai ad Julius Fergy T. Rabago Departmet
More informationGenerating Functions for Laguerre Type Polynomials. Group Theoretic method
It. Joural of Math. Aalysis, Vol. 4, 2010, o. 48, 257-266 Geeratig Fuctios for Laguerre Type Polyomials α of Two Variables L ( xy, ) by Usig Group Theoretic method Ajay K. Shula* ad Sriata K. Meher** *Departmet
More informationIN 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 informationDYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS
DYNAMIC ANALYSIS OF BEAM-LIKE STRUCTURES SUBJECT TO MOVING LOADS Ivaa Štimac 1, Ivica Kožar 1 M.Sc,Assistat, Ph.D. Professor 1, Faculty of Civil Egieerig, Uiverity of Rieka, Croatia INTRODUCTION The vehicle-iduced
More informationf(w) w z =R z a 0 a n a nz n Liouville s theorem, we see that Q is constant, which implies that P is constant, which is a contradiction.
Theorem 3.6.4. [Liouville s Theorem] Every bouded etire fuctio is costat. Proof. Let f be a etire fuctio. Suppose that there is M R such that M for ay z C. The for ay z C ad R > 0 f (z) f(w) 2πi (w z)
More informationPAijpam.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 informationThe Adomian Polynomials and the New Modified Decomposition Method for BVPs of nonlinear ODEs
Mathematical Computatio March 015, Volume, Issue 1, PP.1 6 The Adomia Polyomials ad the New Modified Decompositio Method for BVPs of oliear ODEs Jusheg Dua # School of Scieces, Shaghai Istitute of Techology,
More informationTHE KALMAN FILTER RAUL ROJAS
THE KALMAN FILTER RAUL ROJAS Abstract. This paper provides a getle itroductio to the Kalma filter, a umerical method that ca be used for sesor fusio or for calculatio of trajectories. First, we cosider
More informationUnit 4: Polynomial and Rational Functions
48 Uit 4: Polyomial ad Ratioal Fuctios Polyomial Fuctios A polyomial fuctio y px ( ) is a fuctio of the form p( x) ax + a x + a x +... + ax + ax+ a 1 1 1 0 where a, a 1,..., a, a1, a0are real costats ad
More informationApply change-of-basis formula to rewrite x as a linear combination of eigenvectors v j.
Eigevalue-Eigevector Istructor: Nam Su Wag eigemcd Ay vector i real Euclidea space of dimesio ca be uiquely epressed as a liear combiatio of liearly idepedet vectors (ie, basis) g j, j,,, α g α g α g α
More informationThe Phi Power Series
The Phi Power Series I did this work i about 0 years while poderig the relatioship betwee the golde mea ad the Madelbrot set. I have fially decided to make it available from my blog at http://semresearch.wordpress.com/.
More informationSome Variants of Newton's Method with Fifth-Order and Fourth-Order Convergence for Solving Nonlinear Equations
Copyright, Darbose Iteratioal Joural o Applied Mathematics ad Computatio Volume (), pp -6, 9 http//: ijamc.darbose.com Some Variats o Newto's Method with Fith-Order ad Fourth-Order Covergece or Solvig
More informationMatrix representations of Fibonacci-like sequences
NTMSCI 6, No. 4, 03-0 08 03 New Treds i Mathematical Scieces http://dx.doi.org/0.085/tmsci.09.33 Matrix represetatios of Fiboacci-like sequeces Yasemi Tasyurdu Departmet of Mathematics, Faculty of Sciece
More informationPrecalculus MATH Sections 3.1, 3.2, 3.3. Exponential, Logistic and Logarithmic Functions
Precalculus MATH 2412 Sectios 3.1, 3.2, 3.3 Epoetial, Logistic ad Logarithmic Fuctios Epoetial fuctios are used i umerous applicatios coverig may fields of study. They are probably the most importat group
More informationME NUMERICAL METHODS Fall 2007
ME - 310 NUMERICAL METHODS Fall 2007 Group 02 Istructor: Prof. Dr. Eres Söylemez (Rm C205, email:eres@metu.edu.tr ) Class Hours ad Room: Moday 13:40-15:30 Rm: B101 Wedesday 12:40-13:30 Rm: B103 Course
More informationNew Results for the Fibonacci Sequence Using Binet s Formula
Iteratioal Mathematical Forum, Vol. 3, 208, o. 6, 29-266 HIKARI Ltd, www.m-hikari.com https://doi.org/0.2988/imf.208.832 New Results for the Fiboacci Sequece Usig Biet s Formula Reza Farhadia Departmet
More information