Operational Tau method for singular system of Volterra integro-differential equations

被引：13

作者：

Pishbin, S. ^{[1
]}

机构：

[1] Urmia Univ, Fac Sci, Dept Math, POB 165, Orumiyeh, Iran

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2017年 / 311卷

关键词：

Singular system of Volterra integro-differential equations; nu-smoothing Volterra operator; Legendre spectral Tau methods; Error analysis; INTEGRAL-ALGEBRAIC EQUATIONS; CONVERGENCE ANALYSIS; COLLOCATION METHODS; NUMERICAL-SOLUTION;

D O I：

10.1016/j.cam.2016.07.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Legendre spectral Tau matrix formulation is proposed to approximate solution of singular system of Volterra integro-differential equations. The existence and uniqueness solution of this system are investigated by means of the nu-smoothing property of a Volterra integral operator and some projectors. The L-2-convergence of the numerical method is analyzed. It is proved theoretically and demonstrated numerically that the proposed method converges exponentially. Finally, two numerical examples illustrate the theoretical results. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：205 / 214

页数：10

共 50 条

[1] A METHOD FOR THE SOLUTION OF A CLASS OF SINGULAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
PROSPERETTI, A
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 1982, 46 (03) : 462 - 468
[2] Numerical analysis of an operational Jacobi Tau method for fractional weakly singular integro-differential equations
Mokhtary, P.
[J]. APPLIED NUMERICAL MATHEMATICS, 2017, 121 : 52 - 67
[3] Numerical solution of the system of nonlinear Volterra integro-differential equations with nonlinear differential part by the operational Tau method and error estimation
Abbasbandy, S.
Taati, A.
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 231 (01) : 106 - 113
[4] Numerical solution of the nonlinear Volterra integro-differential equations by the Tau method
Ebadi, G.
Rahimi-Ardabili, M. Y.
Shahmorad, S.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (02) : 1580 - 1586
[5] Spectral collocation method for weakly singular Volterra integro-differential equations
Gu, Zhendong
[J]. APPLIED NUMERICAL MATHEMATICS, 2019, 143 : 263 - 275
[6] A matrix formulation of the Tau Method for Fredholm and Volterra linear integro-differential equations
AliAbadi, M. Hosseini
Shahmorad, S.
[J]. Korean Journal of Computational and Applied Mathematics, 2002, 9 (02): : 497 - 507
[7] A matrix formulation of the Tau Method for Fredholm and Volterra linear integro-differential equations
Hosseini Ali Abadi, M.
Shahmorad, S.
[J]. Journal of Applied Mathematics and Computing, 2002, 9 (02) : 497 - 507
[8] A matrix formulation of the tau method for fredholm and Volterra linear integro-differential equations
Ali Abadi M.
Shahmorad S.
[J]. Journal of Applied Mathematics and Computing, 2002, 9 (2) : 497 - 507
[9] Legendre wavelets operational method for the numerical solutions of nonlinear Volterra integro-differential equations system
Sahu, P. K.
Ray, S. Saha
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 256 : 715 - 723
[10] An Operational Matrix Method for Solving Delay Fredholm and Volterra Integro-Differential Equations
Shahmorad, Sedaghat
Ostadzad, Mohammad Hossein
[J]. INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2016, 13 (06)

← 1 2 3 4 5 →