Adaptive collocation methods for Volterra integral and integro-differential equations

被引：3

作者：

Jiang, Yingjun ^{[1
]}

机构：

[1] Changsha Univ Sci & Technol, Dept Math & Sci Computing, Changsha 410076, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2007年 / 191卷 / 01期

关键词：

Volterra integral equations; Volterra integro-differential equations; collocation methods; a posteriori error estimate;

D O I：

10.1016/j.amc.2006.12.087

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the a posteriori error estimates of collocation methods are derived for Volterra integral and integro-differential equations with smooth and weakly singular kernels. The derived error indicators are constructed in an iterative way and used to adaptively re. ne the meshes in the ports of large gradients. This approach is much more efficient than the collocation methods on the fixed meshes. Numerical computations confirm the analysis via several examples. (c) 2007 Published by Elsevier Inc.

引用

页码：67 / 78

页数：12

共 50 条

[31] The spectral methods for parabolic Volterra integro-differential equations
Fakhar-Izadi, Farhad
Dehghan, Mehdi
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (14) : 4032 - 4046
[32] LINEAR MULTISTEP METHODS FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
LINZ, P
JOURNAL OF THE ACM, 1969, 16 (02) : 295 - &
[33] Bifurcations in numerical methods for Volterra integro-differential equations
Edwards, JT
Ford, NJ
Roberts, JA
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (11): : 3255 - 3271
[34] NUMERICAL METHODS FOR NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
FELDSTEI.A
SOPKA, JR
SIAM REVIEW, 1969, 11 (01) : 111 - &
[35] Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels
Brunner, H
Pedas, A
Vainikko, G
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2001, 39 (03) : 957 - 982
[36] Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations
Wei, Yunxia
Chen, Yanping
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2011, 4 (03) : 419 - 438
[37] Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations
Driscoll, Tobin A.
JOURNAL OF COMPUTATIONAL PHYSICS, 2010, 229 (17) : 5980 - 5998
[38] On the attainable order of collocation methods for pantograph integro-differential equations
Muroya, Y
Ishiwata, E
Brunner, H
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 152 (1-2) : 347 - 366
[39] The Discretization of Neutral Functional Integro-Differential Equations by Collocation Methods
Brunner, H.
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 1999, 18 (02): : 393 - 406
[40] Iterative Collocation Method for Second-Order Volterra Integro-Differential Equations
Rouibah, Khaoula
Bellour, Azzeddine
Laib, Hafida
INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS, 2025,

← 1 2 3 4 5 →