# 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)
• Published : 2016.01.31
• 152 28

#### 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

#### Acknowledgement

Supported by : NSFC, Hunan Provincial Science and Technology Department

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