JACOBI SPECTRAL GALERKIN METHODS FOR VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNEL

Title & Authors
JACOBI SPECTRAL GALERKIN METHODS FOR VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNEL
Yang, Yin;

Abstract
We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations (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 $\small{L^{\infty}}$ norm and weighted $\small{L^2}$-norm. The numerical examples are given to illustrate the theoretical results.
Keywords
spectral Galerkin methods;Jacobi polynomial;Volterra integral equations with weakly singular kernels;
Language
English
Cited by
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2.
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3.
Spectral collocation method for the time-fractional diffusion-wave equation and convergence analysis, Computers & Mathematics with Applications, 2017, 73, 6, 1218
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