Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Convergence analysis of spectral galerkin methods for volterra type integral equations

Language

English

Abstract

This work is to provide spectral and pseudo-spectral Jacobi-Galerkin approaches for the second kind Volterra integral equation. The Gauss-Legendre quadrature formula is used to approximate the integral operator and the inner product based on the Jacobi weight is implemented in the weak formulation in the numerical implementation. For some spectral and pseudo-spectral Jacobi-Galerkin methods, a rigorous error analysis in both the infinity and weighted norms is given provided that both the kernel function and the source function are sufficiently smooth. Numerical experiments validate the theoretical prediction. © Springer Science+Business Media, LLC 2012.

Keywords

Pseudo-spectral Galerkin, Spectral convergence, Spectral Galerkin, The second kind Volterra integral equations

Publication Date

2012

Source Publication Title

Journal of Scientific Computing

Volume

53

Issue

2

Start Page

414

End Page

434

Publisher

Springer

DOI

10.1007/s10915-012-9577-8

Link to Publisher's Edition

http://dx.doi.org/10.1007/s10915-012-9577-8

ISSN (print)

08857474

ISSN (electronic)

15737691

This document is currently not available here.

Share

COinS