Petrov-galerkin methods for nonlinear volterra integro-differential equations

Tao Lin, Yanping Lin, Ping Luo, Ming Rao, Shuhua Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)

Abstract

This paper presents a class of Petrov-Galerkin finite element (PGFE) methods for the initial-value problem for nonlinear Volterra integro-differential equations: y′(t) = f(t, y(t)) + ∫0t k(t, s, y(s))ds, t ∈ I := [0, T], y(0) = 0. These methods have global optimal convergence rates, and have certain global and local super-convergence features. Several post-processing techniques are proposed to obtain globally super-convergent approximations. As by products, these super-convergent approximations can be used as efficient a-posteriori error estimators. Numerical examples are provided to illustrate properties of these methods.
Original languageEnglish
Pages (from-to)405-426
Number of pages22
JournalDynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm
Volume8
Issue number3
Publication statusPublished - 1 Sep 2001
Externally publishedYes

Keywords

  • A-posteriori error estimators
  • Interpolation post-processing
  • Optimal error estimates
  • Petrov-Galerkin finite element methods
  • Volterra integro-differential equations

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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