Numerical solution of high-order linear Volterra integro-differential equations by using Taylor collocation method

被引：9

作者：

Laib, Hafida ^{[1
,3
]}

Bellour, Azzeddine ^{[2
]}

Bousselsal, Mahmoud ^{[3
]}

机构：

[1] Ctr Univ Mila, Inst Sci & Technol, Mila, Algeria

[2] Ecole Normale Super Constantine, Dept Math, Constantine, Algeria

[3] Ecole Normale Super, Lab Anal Nonlineaire & HM, Algiers, Algeria

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2019年 / 96卷 / 05期

关键词：

High-order linear Volterra integro-differential equation; collocation method; Taylor polynomials; convergence analysis; INTEGRAL-EQUATIONS; CONVERGENCE;

D O I：

10.1080/00207160.2018.1484112

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The main purpose of this work is to provide a new direct numerical method for high-order linear Volterra integro-differential equations (VIDEs). An algorithm based on the use of Taylor polynomials is developed for the numerical solution of high-order linear VIDEs. It is shown that this algorithm is convergent. Numerical results are presented and comparisons are made with well-known numerical methods to prove the effectiveness of the presented algorithm.

引用

页码：1066 / 1085

页数：20

共 36 条

[1] COLLOCATION METHODS FOR 2ND-ORDER VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
AGUILAR, M
BRUNNER, H
[J]. APPLIED NUMERICAL MATHEMATICS, 1988, 4 (06) : 455 - 470
[2] [Anonymous], 2010, Seven lectires on theory and numerical solution of Volterra integral equations
[3] [Anonymous], 2000, DIFFERENCE EQUATIONS
[4] TRAVELLING WAVES FOR INTEGRO-DIFFERENTIAL EQUATIONS IN POPULATION DYNAMICS
Apreutesei, Narcisa
Ducrot, Arnaud
Volpert, Vitaly
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2009, 11 (03): : 541 - 561
[5] Numerical solution of Volterra integral and integro-differential equations of convolution type by using operational matrices of piecewise constant orthogonal functions
Babolian, E.
Shamloo, A. Salimi
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 214 (02) : 495 - 508
[6] Numerical solution of delay integro-differential equations by using Taylor collocation method
Bellour, Azzeddine
Bousselsal, Mahmoud
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2014, 37 (10) : 1491 - 1506
[7] A Taylor collocation method for solving delay integral equations
Bellour, Azzeddine
Bousselsal, Mahmoud
[J]. NUMERICAL ALGORITHMS, 2014, 65 (04) : 843 - 857
[8] BRUNNER H, 1984, MATH COMPUT, V42, P95, DOI 10.1090/S0025-5718-1984-0725986-6
[9] POLYNOMIAL SPLINE COLLOCATION METHODS FOR VOLTERRA INTEGRODIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS
BRUNNER, H
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 1986, 6 (02) : 221 - 239
[10] Brunner H., 1973, BIT (Nordisk Tidskrift for Informationsbehandling), V13, P381, DOI 10.1007/BF01933399

← 1 2 3 4 →