Bull. Korean Math. Soc. 2016; 53(1): 247-262
Printed January 31, 2016
https://doi.org/10.4134/BKMS.2016.53.1.247
Copyright © The Korean Mathematical Society.
Yin Yang
Xiangtan University
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
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd