Petrov-Galerkin methods for linear Volterra integro-differential equations

被引：53

作者：

Lin, T ^{[1
]}

Lin, YP

Rao, M

Zhang, SH

机构：

[1] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

[2] Univ Alberta, Dept Math Sci, Edmonton, AB T6G 2G1, Canada

[3] Univ Alberta, Dept Chem & Mat Engn, Edmonton, AB T6G 2G2, Canada

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2000年 / 38卷 / 03期

关键词：

Volterra integro-differential equations; Petrov-Galerkin methods; asymptotic expansions; defect correction; interpolation postprocessing; a posteriori error estimators;

D O I：

10.1137/S0036142999336145

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a class of Petrov Galerkin solutions that have global optimal convergence rates for linear Volterra integro-differential equations. These solutions also possess certain local and global superconvergence. Asymptotic expansions of the errors in these solutions are established which can be used to form higher order approximations by Richardson extrapolation and defect corrections. Several postprocessing techniques are introduced to enhance these solutions. As by-products, these higher order numerical approximations can be used to generate a posteriori error estimators. Representative numerical results are also provided.

引用

页码：937 / 963

页数：27

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