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http://dx.doi.org/10.4134/BKMS.2016.53.1.247

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

Yang, Yin (Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.1, 2016 , pp. 247-262 More about this Journal
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 $L^{\infty}$ 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;
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