Matrix Form of Legendre Polynomials for Solving Linear Integro-Differential Equations of High Order

被引：0

作者：

Kammuji, M. ^{[1
]}

Eshkvatov, Z. K. ^{[1
,2
]}

Yunus, Arif A. M. ^{[1
]}

机构：

[1] Univ Sains Islam Malaysia, Fac Sci & Technol, Negeri Sembilan, Malaysia

[2] Univ Putra Malaysia, Inst Math Res INSPEM, Serdang, Malaysia

来源：

4TH INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES (ICMS4): MATHEMATICAL SCIENCES: CHAMPIONING THE WAY IN A PROBLEM BASED AND DATA DRIVEN SOCIETY | 2017年 / 1830卷

关键词：

NUMERICAL-SOLUTION;

D O I：

10.1063/1.4980919

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transtbnn FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods

引用

页数：9

共 17 条

[1] A Chebyshev polynomial approach for linear Fredholm-Volterra integro-differential equations in the most general form
Akyuz-Dascioglu, Aysegul
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 181 (01) : 103 - 112
[2] Approximate solutions of Fredholm integral equations of the second kind
Chakrabarti, A.
Martha, S. C.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2009, 211 (02) : 459 - 466
[3] Solution of an integro-differential equation arising in oscillating magnetic fields using He's homotopy perturbation method
Dehghan, M.
Shakeri, F.
[J]. PROGRESS IN ELECTROMAGNETICS RESEARCH-PIER, 2008, 78 : 361 - 376
[4] Eshkuvatov Z. K., AIMS J SUBMITTED
[5] Hock P. Y., 2000, LLJABAR LINEAR PERMU, P34
[6] Approximate solution of a class of linear integro-differential equations by Taylor expansion method
Huang, Y.
Li, X. -F.
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (06) : 1277 - 1288
[7] Numerical solution of a Fredholm integro-differential equation modelling θ-neural networks
Jackiewicz, Z.
Rahman, M.
Welfert, B. D.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2008, 195 (02) : 523 - 536
[8] Kythe P. K., 2004, HDB COMPUTATION LEHO, P115
[9] Liu N., 2008, THESIS, P6
[10] Discussion on convergence of Legendre polynomial for numerical solution of integral equations
Maleknejad, K.
Nouri, K.
Yousefi, M.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 193 (02) : 335 - 339

← 1 2 →