Convergence Analysis of Spectral Galerkin Methods for Volterra Type Integral Equations

Authors:
Ziqing Xie;Xianjuan Li;Tao Tang
Affiliations:
School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, China 550001 and Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Edu ...;School of Mathematics, Fuzhou University, Fuzhou, China 350002;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
Venue:
Journal of Scientific Computing
Year:
2012

Citing 3
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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.