Petrov-Galerkin methods for linear Volterra integro-differential equations

Tao Lin, Yanping Lin, Ming Rao, Shuhua Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

48 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)937-963
Number of pages27
JournalSIAM Journal on Numerical Analysis
Volume38
Issue number3
DOIs
Publication statusPublished - 1 Dec 2001
Externally publishedYes

Keywords

  • A posteriori error estimators
  • Defect correction
  • Interpolation postprocessing
  • Petrov-Galerkin methods, asymptotic expansions
  • Volterra integro-differential equations

ASJC Scopus subject areas

  • Numerical Analysis

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