Jacobi spectral Galerkin methods for Volterra integral equations with weakly singular kernel
Bull. Korean Math. Soc. 2016 Vol. 53, No. 1, 247-262
https://doi.org/10.4134/BKMS.2016.53.1.247
Printed January 31, 2016
Yin Yang
Xiangtan University
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.
Keywords : spectral Galerkin methods, Jacobi polynomial, Volterra integral equations with weakly singular kernels
MSC numbers : Primary 65R20, 45J05, 65N12
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