Exact Solutions of the Generalized Benjamin Equation and (3 + 1)- Dimensional Gkp Equation by the Extended Tanh Method
|
|
- Madlyn Ilene Clark
- 5 years ago
- Views:
Transcription
1 Available at Appl Appl Math ISSN: Vol 7, Issue (Jue 0), pp Applicatios ad Applied Mathematics: A Iteratioal Joural (AAM) Exact Solutios of the Geeralized Bejami Equatio ad (3 + )- Dimesioal Gkp Equatio by the Exteded Tah Method N Taghizadeh, M Mirzazadeh ad SR Moosavi Noori Departmet of Pure Mathematics Uiversity of Guila PO Box 94, Rasht, Ira taghizadeh@guilaacir; mirzazadehs@guilaacir moosavioori@mscguilaacir Abstract Received: May 4, 0; Accepted: April 4, 0 I this paper, the exteded tah method is used to costruct exact solutios of the geeralized Bejami ad (3 + )-dimesioal gkp equatio This method is show to be a efficiet method for obtaiig exact solutios of oliear partial differetial equatios It ca be applied to oitegrable equatios as well as to itegrable oes Keywords: Exteded tah method; Geeralized Bejami equatio; (3+)-dimesioal gkp equatio MSC 00: 47F05, 35G0 Itroductio It is well kow that the oliear partial differetial equatios (NLPDEs) are widely used to describe complex pheomea i various fields of scieces, such as physics, biology, chemistry, etc Therefore, seekig exact solutios of NLPDEs is very importat ad sigificat i the oliear scieces I the past decades, great effort has bee made towards this task ad may powerful methods have bee preseted, such as the homogeeous balace method [Khalafallah (009) ad Wag (995, 996)], the modified simplest equatio method [Kudryashov ad Loguiova (008)], the tah method [Malfliet ad Herema (99, 996)], the exteded tah 75
2 76 N Taghizadeh, M Mirzazadeh ad SR Moosavi Noori method [Taghizadeh et al (0) ad Wazwaz (007, 008)], the Jacobia elliptic fuctio expasio method [Liu et al (00)], the first itegral method [Feg et al (00, 005)], ad so o I recet years, may authors have used the exteded tah method to obtai the exact solutios of partial differetial equatios as the method is deemed a efficiet method for obtaiig exact solutios of NLPDEs The aim of this paper is to fid exact solito solutios of the geeralized Bejami equatio ad (3 + )-dimesioal gkp equatio, usig the exteded tah method The Exteded Tah Method ad Tah Method A PDE Fuu (, x, ut, uxx, uxt, uxxx,) 0, () ca be coverted to a ODE Guu (, ', u'', u''',) 0, () upo usig a wave variable x t Eq () is the itegrated as log as all terms cotai derivatives where the itegratio costats are cosidered zeros The stadard tah method is developed by Malfliet [9 ] where the tah is used as a ew variable, sice all derivatives of a tah are represeted by a tah itself Itroducig a ew idepedet variable Y tah( ), x t, (3) leads to the chage of derivatives: d d d dy ( Y ), d Y ( Y ) d ( Y ) d (4) d dy dy The exteded tah method admits the use of the fiite expasio M M k k k (5) k 0 k k u( ) S( Y ) ay b Y,
3 AAM: Iter J, Vol 7, Issue (Jue 0) 77 where M is a positive iteger, i most cases, that will be determied Expasio (5) reduces to the stadard tah method for bk 0, ( k,, M ) Substitutig (5) ito the ODE () results i a algebraic equatio i powers of Y To determie the parameter M, we usually balace the liear terms of highest order i the resultig equatio with the highest order oliear terms We the collect all coefficiets of powers of Y i the resultig equatio where these coefficiets have to vaish This will give a system of algebraic equatios ivolvig the parameters ak ( k 0,, M), bk ( k,, M ), ad Havig determied these parameters we obtai a aalytic solutio u( x, t ) i a closed form 3 Exact Solutios of the Geeralized Bejami Equatio Let us cosider the geeralized Bejami equatio: u ( u u ) u 0, (6) tt x x xxxx where ad are costats This kid of equatio is oe of the most importat NLPDEs, used i the aalysis of log wave i shallow water [Herema et al (986)] By usig the wave variable u( x, t) U ( ), k( x t), (6) becomes the ODE 4 k U ku U k U '' ( ')' '''' 0 (7) Itegratig Equatio (7), twice ad settig the costat of itegratig to zero, we have k '' 0 4 k U U k U (8) Balacig U '' with U i Equatio (8) gives M ( ) M, the M To get a closed form solutio, M should be a iteger To achieve our goal, we use the Trasformatio U( ) V ( ) (9)
4 78 N Taghizadeh, M Mirzazadeh ad SR Moosavi Noori This trasformatio (9) chages Equatio (8) ito the ODE 3 3 k V V k V VV ( ) [( ) ' ( ) ''] 0 (0) Balacig so VV '' with M 3 M, M 3 V i Equatio (0) gives I this case, the exteded tah method i the form (5) admits the use of the fiite expasio b b U( ) S( Y ) a 0 ay ay Y Y () Substitutig the form () ito Equatio (0) ad usig (4), while collectig the coefficiets of Y we obtai: 6 a k ( )( ) a aa 4 k ( ) aa 3 4 k ( ) a 3 [ a a a a ] k ( )[( ) a 8a 6 a a ] k ( ) aa 3 [ a b a aa ] a ( )[ ( 4) (5 ) ] k a0a aa ab
5 AAM: Iter J, Vol 7, Issue (Jue 0) 79 k ( )[ a a a ] 3 [ a a a a a b aa b] k ( )[ a ( ) a 4 a a () ab 4() a b ] 3 0 k ( )[ a a a b] 3 [ a a a b a a b aa b] k ( )[ a0a ( ) aa (9 4) ab ( ) ab ] 0 k ( )[ a ab a b ] 3 [ a b a b a ab a a b ] ( )( )[ ] a0 k ( )[ aa 0 ab 0 ( ) ab 8( ) ab ] 3 k a b Y : k ( )[ a b ab ] 3 [ a b ab a ab a bb ] ( )[ ( ) (9 4) ( ) ] k a0b bb ab ab Y : k ( )[ b a b ] 3 [ a b a b a b abb ] k ( )[ b ( ) b 4 a b () ab 4() a b ] Y : k ( ) bb 3 [ ab a bb ] b ( )[ ( 4) (5 ) ] k a0b bb ab 4 Y : k ( ) b 3 [ ab b b ] k ( )[( ) b 8b 6 ab ] Y :
6 80 N Taghizadeh, M Mirzazadeh ad SR Moosavi Noori 3bb 4 k ( ) bb 3 6 Y : b k ( )( ) b 3 3 Settig these coefficiets equal to zero, ad solvig the resultig system, by usig Maple, we fid the followig sets of solutios: a 0 k( )( ), a 0, a k( )( ), b 0, b 0, k () a 0 k( )( ), a 0, a 0, b 0, b k( )( ), k (3) a 0 k( )( ), a 0, 4 a 8 k( )( ), b 0, b 8 k( )( ), 4 k (4) Recall that U V For 0, the sets ()-(4) give the solitos solutios k( )( ) u( x, t) { sec h [ ( x t)]}, (5)
7 AAM: Iter J, Vol 7, Issue (Jue 0) 8 k( )( ) u( x, t) { csc h [ ( x t)]}, k( )( ) u3( x, t) { (tah [ ( x t)] coth [ ( )])} x t (6) (7) However for 0, we obtai the travellig wave solutios k( )( ) u4( x, t) { sec [ ( x t)]}, (8) k( )( ) u5( x, t) { csc [ ( x t)]}, (9) k( )( ) u6( x, t) { (ta [ ( x t)] cot [ ( x t)])} (0) 4 The (3 + )-dimesioal gkp Equatio The (3 + )-dimesioal gkp equatio, give by ( u 6 u u u ) 3u 3u 0, () t x xxx x yy zz describes the dyamics of solitos ad oliear waves i plasmas physics ad fluid dyamics [Alagesa et al(997)] By usig the wave trasformatio u( x, y, z, t) U ( ), k( x ly mz t), carries Equatio () ito the ODE (3 3 ) '' 6 l m U U U '' 6 U ( U ') k U '''' 0 () Twice itegratig of Equatio (), settig the costat of itegratig to zero, we will have
8 8 N Taghizadeh, M Mirzazadeh ad SR Moosavi Noori 6 l m U U k U (3 3 ) '' 0 (3) Balacig the U '' with U M ( ) M, i Equatio (3) gives M To get a closed form solutio, M should be a iteger To achieve our goal, we use the Trasformatio U( ) V ( ) (4) This trasformatio (4) will chage Equatio (3) ito the ODE ( )(3 3 ) 6 [( ) ' ( ) ''] 0 (5) 3 l m V V k V VV Balacig the VV '' with M 3 M, M 3 V i Equatio (5) gives I this case, the exteded tah method the form (5) admits the use of the fiite expasio b b U( ) S( Y ) a 0 ay ay Y Y (6) Substitutig the form (6) ito Equatio (5) ad usig (4), collectig the coefficiets of Y we obtai: 6 6a k ( )( ) a 3 5
9 AAM: Iter J, Vol 7, Issue (Jue 0) 83 8aa 4 k ( ) aa 4 ( )(3l 3 m ) a 8 [ a a a a ] 0 k ( )[( ) a 8a 6 a a ] 0 3 ( )(3l 3 m ) aa 8 [ a b aaa ] 6 a ( )[ ( 4) (5 ) ] 3 0 k a0a aa ab ( )(3l 3 m )[ a a a ] 8 [ a a a a a b aa b] ( )[ ( ) 4 ( ) 4( ) ] k a a a0a ab ab ( )(3l 3 m )[ aa ab] 8 [ aa abaab aab] ( )[ ( ) (9 4) ( ) ] k a0a aa ab ab 0 ( )(3l 3 m )[ a ab ab] 8 [ ab ab aab aab] 6 ( )[ ( ) 8( ) ] ( )( )[ ] a0 k aa 0 ab 0 ab ab k a b Y : ( )(3l 3 m )[ ab ab ] 8 [ a b ab a ab abb ] ( )[ ( ) (9 4) ( ) ] k a0b bb ab ab Y :
10 84 N Taghizadeh, M Mirzazadeh ad SR Moosavi Noori ( )(3l 3 m )[ b a b ] 8 [ a b a b a b abb ] k ( )[ b ( ) b 4 a b () ab 4() a b ] 0 3 Y : ( )(3l 3 m ) bb 8 [ ab a bb ] 6 b ( )[ ( 4) (5 ) ] 3 0 k a0b bb ab 4 Y : ( )(3l 3 m ) b 8 [ a b b b ] ( )[( ) 8 6 ] 0 k b b a0b 5 Y : 8bb 4 k ( ) bb 6 Y : 6b k ( )( ) b 3 Settig these coefficiets equal to zero, ad solvig the resultig system, by usig Maple, we fid the followig sets of solutios: a0 (3 l 3 m )( )( ), a 0, (3 3 )( )( ), a l m b 0, b 0, (7) 3m 3l k a0 (3 l 3 m )( )( ), a 0, a 0, b 0, (8)
11 AAM: Iter J, Vol 7, Issue (Jue 0) 85 (3 3 )( )( ), b l m 3m 3l k a0 (3 l 3 m )( )( ), a 0, 4 (3 3 )( )( ), a l m b 0, (9) 48 (3 3 )( )( ), b l m 48 Recall that 3m 3l 4 k U V For 3m 3l 0, the sets (7)-(9) give the solitos solutios u x y z t l m (,,, ) { (3 3 )( )( ) 3m 3l h k u( x, y, z, t) { (3l 3 m )( )( ) sec [ ]}, 3m 3l k csc [ ]}, u x y z t l m 48 3(,,, ) { (3 3 )( )( ) h 3m 3l 4 k ( tah [ ] 3m 3l 4 k coth [ ])}, (30) (3) (3) where k( x ly mz t)
12 86 N Taghizadeh, M Mirzazadeh ad SR Moosavi Noori However, for 3m 3l 0, we obtai the travellig wave solutios 3l 3m u4( x, y, z, t) { (3l 3 m )( )( )sec [ ]}, k 3l 3m u5( x, y, z, t) { (3l 3 m )( )( ) csc [ ]}, k u x y z t l m 48 6(,,, ) { (3 3 )( )( ) 3l 3m 3l 3m ( ta [ ] cot [ ])}, 4 k 4 k (35) where k( x ly mz t) (33) (34) 5 Coclusio The exteded tah method has bee successfully applied here to fid the exact solutios for geeralized Bejami equatio ad the (3+)-dimesioal gkp equatio It is also evidet that the proposed method ca be exteded to solve the problems of oliear partial differetial equatios arisig i the theory of solitos ad other areas Ackowledgemet The authors would like to express sicerely thaks to the referees for their useful ad valuable commets REFERENCES Alagesa, T, Uthayakumar, A ad Porsezia, K (997) Pailev aalysis ad Backlud trasformatio for a three-dimesioal Kadomtsev-Petviashvili equatio, Chaos Solitos Fractals, Vol 8, pp Feg, ZS (00) The first itegral method to study the Burgers-Kortewegde Vries equatio, J Phys A, Vol 35, No, pp Feg, ZS ad Wag, XH (00) The first itegral method to the two dimesioal Burgers- KdV equatio, Phys Lett A, Vol 308, pp 73-78
13 AAM: Iter J, Vol 7, Issue (Jue 0) 87 Feg, ZS ad Che, G (005) Solitary wave solutios of the compoud Burgers-Korteweg-de Vries equatio, Physica A, Vol 35, pp Herema, W, Baerjee, P P, Korpel, A, Assato, G, Va Immerzeele, A ad Meerpole, A (986) Exact solitary wave solutios of oliear evolutio ad wave equatios usig a direct algebraic method, J Phys A Math Ge Vol 9, No 5, pp Khalfallah, M (009) New exact travellig wave solutios of the (3+) dimesioal Kadomtsev-Petviashvili (KP) equatio, Commu Noliear Sci Numer Simul, Vol 4, pp Kudryashov, NA ad Loguiova, NB (008) Exteded simplest equatio method for oliear differetial equatios, Appl Math Comput, Vol 05, pp Liu, SK Fu, Z Liu, SD ad Zhao, Q (00) Jacobi elliptic fuctio method ad periodic wave solutios of oliear wave equatios, Phys Lett A, Vol 89, pp Malfliet, W (99) Solitary wave solutios of oliear wave equatios, Am J Phys, Vol 60, No 7, pp Malfliet, W ad Herema, W (996) The tah method: I Exact solutios of oliear evolutio ad wave equatios, Phys Scripta, Vol 54, pp Malfliet, W ad Herema, W (996) The tah method: II Perturbatio techique for coservative systems, Phys Scripta, Vol 54, pp Taghizadeh, N Mirzazadeh, M ad Moosavi Noori, SR (0) Exact solutios of (+)- dimesioal oliear evolutio equatios by usig the exteded tah method, Aust J Basic & Appl Sci Vol 5, No 6, pp Wag, ML (995) Solitrary wave solutio for variat Boussiesq equatio, Phys Lett A, Vol 99, pp 69-7 Wag, ML (996) Applicatia of homogeeous balace method to exact solutios of oliear equatio i mathematical physics, Phys Lett A, Vol 6, pp Wazwaz, AM (007) The exteded tah method for abudat solitary wave solutios of oliear wave equatios, Appl Math Comput Vol 87, pp 3-4 Wazwaz, AM (008) The exteded tah method for the Zakharov-Kuzetsov (ZK) equatio, the modified ZK equatio, ad its geeralized forms, Commu Noliear Sci Numer Simulat, Vol 3, pp
The Solutions of Nonlinear Heat Conduction Equation via Fibonacci&Lucas Approximation Method. Zehra Pınar a. Turgut Öziş b.
The Solutios of Noliear Heat Coductio Equatio via Fiboacci&Lucas Approximatio Method Zehra Pıar a Turgut Öziş b a Namık Kemal Uiversity, Faculty of Sciece & Letters, Departmet of Mathematics,, 59030 Tekirdağ,
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 informationModified 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 informationCNOIDAL WAVES, SOLITARY WAVES AND PAINLEVE ANALYSIS OF THE 5TH ORDER KDV EQUATION WITH DUAL-POWER LAW NONLINEARITY
THE PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY Series A OF THE ROMANIAN ACADEMY Volume 4 Number /03 pp. 8 34 CNOIDAL WAVES SOLITARY WAVES AND PAINLEVE ANALYSIS OF THE 5TH ORDER KDV EQUATION WITH
More informationExact Solutions of the Generalized- Zakharov (GZ) Equation by the Infinite Series Method
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 193-9466 Vol. 05, Issue (December 010), pp. 61 68 (Previously, Vol. 05, Issue 10, pp. 1718 175) Applications and Applied Mathematics: An International
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 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 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 informationMULTIPLE 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 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 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 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 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 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 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 informationThe extended homogeneous balance method and exact 1-soliton solutions of the Maccari system
Computational Methods for Differential Equations http://cmde.tabrizu.ac.ir Vol., No., 014, pp. 83-90 The extended homogeneous balance method and exact 1-soliton solutions of the Maccari system Mohammad
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 informationExact Travelling Wave Solutions of the Coupled Klein-Gordon Equation by the Infinite Series Method
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 93-9466 Vol. 6, Issue (June 0) pp. 3 3 (Previously, Vol. 6, Issue, pp. 964 97) Applications and Applied Mathematics: An International Journal (AAM)
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 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 informationNEW 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 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 informationON SOME TRIGONOMETRIC POWER SUMS
IJMMS 0: 2002 185 191 PII. S016117120200771 http://ijmms.hidawi.com Hidawi Publishig Corp. ON SOME TRIGONOMETRIC POWER SUMS HONGWEI CHEN Received 17 Jue 2001 Usig the geeratig fuctio method, the closed
More informationMost text will write ordinary derivatives using either Leibniz notation 2 3. y + 5y= e and y y. xx tt t
Itroductio to Differetial Equatios Defiitios ad Termiolog Differetial Equatio: A equatio cotaiig the derivatives of oe or more depedet variables, with respect to oe or more idepedet variables, is said
More informationOn the Derivation and Implementation of a Four Stage Harmonic Explicit Runge-Kutta Method *
Applied Mathematics, 05, 6, 694-699 Published Olie April 05 i SciRes. http://www.scirp.org/joural/am http://dx.doi.org/0.46/am.05.64064 O the Derivatio ad Implemetatio of a Four Stage Harmoic Explicit
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 informationChapter 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 informationThe General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method
Applied and Computational Mathematics 015; 4(5): 335-341 Published online August 16 015 (http://www.sciencepublishinggroup.com/j/acm) doi: 10.11648/j.acm.0150405.11 ISSN: 38-5605 (Print); ISSN: 38-5613
More informationIntroducing a Novel Bivariate Generalized Skew-Symmetric Normal Distribution
Joural of mathematics ad computer Sciece 7 (03) 66-7 Article history: Received April 03 Accepted May 03 Available olie Jue 03 Itroducig a Novel Bivariate Geeralized Skew-Symmetric Normal Distributio Behrouz
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 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 informationAdomian Decomposition Method for Solving the Equation Governing the Unsteady Flow of a Polytropic Gas
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 9-966 Vol., Issue (Jue 9) pp. 5 6 (Previousl, Vol., No. ) Applicatios ad Applied Mathematics: A Iteratioal Joural (AAM) Adomia Decompositio Method
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 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 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 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 informationON SOLVING A FORMAL HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION IN THE COMPLEX FIELD
A. Şt. Uiv. Ovidius Costaţa Vol. (), 003, 69 78 ON SOLVING A FORMAL HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION IN THE COMPLEX FIELD Nicolae Popoviciu To Professor Silviu Sburla, at his 60 s aiversary Abstract
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 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 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 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 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 information1 6 = 1 6 = + Factorials and Euler s Gamma function
Royal Holloway Uiversity of Lodo Departmet of Physics Factorials ad Euler s Gamma fuctio Itroductio The is a self-cotaied part of the course dealig, essetially, with the factorial fuctio ad its geeralizatio
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 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 informationThe Jordan Normal Form: A General Approach to Solving Homogeneous Linear Systems. Mike Raugh. March 20, 2005
The Jorda Normal Form: A Geeral Approach to Solvig Homogeeous Liear Sstems Mike Raugh March 2, 25 What are we doig here? I this ote, we describe the Jorda ormal form of a matrix ad show how it ma be used
More informationQuadratic Transformations of Hypergeometric Function and Series with Harmonic Numbers
Quadratic Trasformatios of Hypergeometric Fuctio ad Series with Harmoic Numbers Marti Nicholso I this brief ote, we show how to apply Kummer s ad other quadratic trasformatio formulas for Gauss ad geeralized
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 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 information1 1 2 = show that: over variables x and y. [2 marks] Write down necessary conditions involving first and second-order partial derivatives for ( x0, y
Questio (a) A square matrix A= A is called positive defiite if the quadratic form waw > 0 for every o-zero vector w [Note: Here (.) deotes the traspose of a matrix or a vector]. Let 0 A = 0 = show that:
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 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 informationPhys. 201 Mathematical Physics 1 Dr. Nidal M. Ershaidat Doc. 12
Physics Departmet, Yarmouk Uiversity, Irbid Jorda Phys. Mathematical Physics Dr. Nidal M. Ershaidat Doc. Fourier Series Deiitio A Fourier series is a expasio o a periodic uctio (x) i terms o a iiite sum
More informationMechanical Quadrature Near a Singularity
MECHANICAL QUADRATURE NEAR A SINGULARITY 215 Mechaical Quadrature Near a Sigularity The purpose of this ote is to preset coefficiets to facilitate computatio of itegrals of the type I x~^fix)dx. If the
More informationSequences of Definite Integrals, Factorials and Double Factorials
47 6 Joural of Iteger Sequeces, Vol. 8 (5), Article 5.4.6 Sequeces of Defiite Itegrals, Factorials ad Double Factorials Thierry Daa-Picard Departmet of Applied Mathematics Jerusalem College of Techology
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 informationSeries with Central Binomial Coefficients, Catalan Numbers, and Harmonic Numbers
3 47 6 3 Joural of Iteger Sequeces, Vol. 5 (0), Article..7 Series with Cetral Biomial Coefficiets, Catala Numbers, ad Harmoic Numbers Khristo N. Boyadzhiev Departmet of Mathematics ad Statistics Ohio Norther
More informationIntegrable Properties Associated with a Discrete Three-by-Three Matrix Spectral Problem
Commu. Theor. Phys. Beijig Chia 52 2009 pp. 981 986 c Chiese Physical Society ad IOP Publishig Ltd Vol. 52 No. 6 December 15 2009 Itegrable Properties Associated with a Discrete Three-by-Three Matrix Spectral
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 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 informationNEW 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 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 informationNumerical Methods in Fourier Series Applications
Numerical Methods i Fourier Series Applicatios Recall that the basic relatios i usig the Trigoometric Fourier Series represetatio were give by f ( x) a o ( a x cos b x si ) () where the Fourier coefficiets
More informationBangi 43600, Selangor Darul Ehsan, Malaysia (Received 12 February 2010, accepted 21 April 2010)
O Cesáro Meas of Order μ for Outer Fuctios ISSN 1749-3889 (prit), 1749-3897 (olie) Iteratioal Joural of Noliear Sciece Vol9(2010) No4,pp455-460 Maslia Darus 1, Rabha W Ibrahim 2 1,2 School of Mathematical
More information8. Applications To Linear Differential Equations
8. Applicatios To Liear Differetial Equatios 8.. Itroductio 8.. Review Of Results Cocerig Liear Differetial Equatios Of First Ad Secod Orders 8.3. Eercises 8.4. Liear Differetial Equatios Of Order N 8.5.
More informationStability Analysis of the Euler Discretization for SIR Epidemic Model
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
More informationCHEBYSHEV WAVELET COLLOCATION METHOD FOR GINZBURG-LANDAU EQUATION
CHEBYSHEV WAVELE COLLOCAION MEHOD FOR GINZBURG-LANDAU EQUAION Aydi SECER * ad Yasemi BAKIR *, Yildiz echical Uiversity, Faculty of Chemistry-Metallurgical, Departmet of Mathematical Egieerig, Davutpaşa
More informationInteresting Series Associated with Central Binomial Coefficients, Catalan Numbers and Harmonic Numbers
3 47 6 3 Joural of Iteger Sequeces Vol. 9 06 Article 6.. Iterestig Series Associated with Cetral Biomial Coefficiets Catala Numbers ad Harmoic Numbers Hogwei Che Departmet of Mathematics Christopher Newport
More informationA Taylor Series Based Method for Solving a Two-dimensional Second-order Equation
Applied Mathematical Scieces, Vol. 8, 2014, o. 66, 3255-3261 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.45347 A Taylor Series Based Method for Solvig a Two-dimesioal Secod-order Equatio
More informationON THE DIOPHANTINE EQUATION
Fudametal Joural of Mathematics ad Mathematical Scieces Vol., Issue 1, 01, Pages -1 This paper is available olie at http://www.frdit.com/ Published olie July, 01 ON THE DIOPHANTINE EQUATION SARITA 1, HARI
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 Algebraic Elimination Method for the Linear Complementarity Problem
Volume-3, Issue-5, October-2013 ISSN No: 2250-0758 Iteratioal Joural of Egieerig ad Maagemet Research Available at: wwwijemret Page Number: 51-55 A Algebraic Elimiatio Method for the Liear Complemetarity
More informationAMS Mathematics Subject Classification : 40A05, 40A99, 42A10. Key words and phrases : Harmonic series, Fourier series. 1.
J. Appl. Math. & Computig Vol. x 00y), No. z, pp. A RECURSION FOR ALERNAING HARMONIC SERIES ÁRPÁD BÉNYI Abstract. We preset a coveiet recursive formula for the sums of alteratig harmoic series of odd order.
More informationLecture 4 Conformal Mapping and Green s Theorem. 1. Let s try to solve the following problem by separation of variables
Lecture 4 Coformal Mappig ad Gree s Theorem Today s topics. Solvig electrostatic problems cotiued. Why separatio of variables does t always work 3. Coformal mappig 4. Gree s theorem The failure of separatio
More informationTHE N-POINT FUNCTIONS FOR INTERSECTION NUMBERS ON MODULI SPACES OF CURVES
THE N-POINT FUNTIONS FOR INTERSETION NUMBERS ON MODULI SPAES OF URVES KEFENG LIU AND HAO XU Abstract. We derive from Witte s KdV equatio a simple formula of the -poit fuctios for itersectio umbers o moduli
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 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 informationThe cosine-function method and the modified extended tanh method. to generalized Zakharov system
Mathematica Aeterna, Vol. 2, 2012, no. 4, 287-295 The cosine-function method and the modified extended tanh method to generalized Zakharov system Nasir Taghizadeh Department of Mathematics, Faculty of
More informationIn algebra one spends much time finding common denominators and thus simplifying rational expressions. For example:
74 The Method of Partial Fractios I algebra oe speds much time fidig commo deomiators ad thus simplifyig ratioal epressios For eample: + + + 6 5 + = + = = + + + + + ( )( ) 5 It may the seem odd to be watig
More informationApplied Mathematics Letters. On the properties of Lucas numbers with binomial coefficients
Applied Mathematics Letters 3 (1 68 7 Cotets lists available at ScieceDirect Applied Mathematics Letters joural homepage: wwwelseviercom/locate/aml O the properties of Lucas umbers with biomial coefficiets
More informationFREE VIBRATIONS OF SIMPLY SUPPORTED BEAMS USING FOURIER SERIES
Abdullah : FREE VIBRATIONS OF SIMPY SUPPORTED BEAMS FREE VIBRATIONS OF SIMPY SUPPORTED BEAMS USING FOURIER SERIES SAWA MUBARAK ABDUAH Assistat ecturer Uiversity of Mosul Abstract Fourier series will be
More informationChapter 8. Euler s Gamma function
Chapter 8 Euler s Gamma fuctio The Gamma fuctio plays a importat role i the fuctioal equatio for ζ(s that we will derive i the ext chapter. I the preset chapter we have collected some properties of the
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 informationThe Analysis of the Non-linear Deflection of Non-straight Ludwick type Beams Using Lie Symmetry Groups
Proceedigs of the 3 rd Iteratioal Coferece o Cotrol, Dyamic Systems, ad Robotics CDSR 16 Ottawa, Caada May 9 10, 016 Paper No. 107 DOI: 10.11159/cdsr16.107 The Aalysis of the No-liear Deflectio of No-straight
More informationSubject: Differential Equations & Mathematical Modeling-III
Power Series Solutios of Differetial Equatios about Sigular poits Subject: Differetial Equatios & Mathematical Modelig-III Lesso: Power series solutios of differetial equatios about Sigular poits Lesso
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 informationAN 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 informationHarmonic balance approaches to the nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable
Joural of Soud ad Vibratio, Vol. 314, Nº 3-5, 775-78 (008) Harmoic balace approaches to the oliear oscillators i which the restorig force is iversely proportioal to the depedet variable A. Belédez, D.
More informationECE-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 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 informationQ-BINOMIALS AND THE GREATEST COMMON DIVISOR. Keith R. Slavin 8474 SW Chevy Place, Beaverton, Oregon 97008, USA.
INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 8 2008, #A05 Q-BINOMIALS AND THE GREATEST COMMON DIVISOR Keith R. Slavi 8474 SW Chevy Place, Beaverto, Orego 97008, USA slavi@dsl-oly.et Received:
More informationLinear Differential Equations of Higher Order Basic Theory: Initial-Value Problems d y d y dy
Liear Differetial Equatios of Higher Order Basic Theory: Iitial-Value Problems d y d y dy Solve: a( ) + a ( )... a ( ) a0( ) y g( ) + + + = d d d ( ) Subject to: y( 0) = y0, y ( 0) = y,..., y ( 0) = y
More informationOn 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 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 informationNew Approach of ( Ǵ/G ) Expansion Method. Applications to KdV Equation
Journal of Mathematics Research; Vol. 6, No. ; ISSN 96-9795 E-ISSN 96-989 Published by Canadian Center of Science and Education New Approach of Ǵ/G Expansion Method. Applications to KdV Equation Mohammad
More informationA note on the p-adic gamma function and q-changhee polynomials
Available olie at wwwisr-publicatioscom/jmcs J Math Computer Sci, 18 (2018, 11 17 Research Article Joural Homepage: wwwtjmcscom - wwwisr-publicatioscom/jmcs A ote o the p-adic gamma fuctio ad q-chaghee
More informationSome families of generating functions for the multiple orthogonal polynomials associated with modified Bessel K-functions
J. Math. Aal. Appl. 297 2004 186 193 www.elsevier.com/locate/jmaa Some families of geeratig fuctios for the multiple orthogoal polyomials associated with modified Bessel K-fuctios M.A. Özarsla, A. Altı
More informationRecursive Algorithms. Recurrences. Recursive Algorithms Analysis
Recursive Algorithms Recurreces Computer Sciece & Egieerig 35: Discrete Mathematics Christopher M Bourke cbourke@cseuledu A recursive algorithm is oe i which objects are defied i terms of other objects
More information