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Jacobi spectral Galerkin methods for Volterra integral equations with weakly singular kernel

Yin Yang
대한수학회 (The Korean Mathematical Society)|2016.01|대한수학회보 (Bulletin of the KMS)|제53권 제1호|pp. 247-262

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참고문헌

키워드

Jacobi polynomialspectral Galerkin methods
주제분류수학

초록

We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations \linebreak (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^\infty$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

Abstract

We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations \linebreak (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^\infty$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

참고문헌 (20)

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