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Spectral method for multidimensional Volterra integral equation with regular kernel

Authors:	Yunxia WEI Yanping CHEN Xiulian SHI Yuanyuan ZHANG

Affiliation:	¹. Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, China². School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China³. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China⁴. Department of Mathematics and Information Science, Yantai University, Yantai 264005, China

Abstract:	This paper is concerned with obtaining an approximate solution for a linear multidimensional Volterra integral equation with a regular kernel. We choose the Gauss points associated with the multidimensional Jacobi weight function $ω (x) = Π i = 1 d (1 − x i) α (1 + x i) β, − 1 < α, β < 1 d − 12$ (d denotes the space dimensions) as the collocation points. We demonstrate that the errors of approximate solution decay exponentially. Numerical results are presented to demonstrate the eectiveness of the Jacobi spectral collocation method.

Keywords:	Multidimensional Volterra integral equation Jacobi collocation discretization multidimensional Gauss quadrature formula
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