RESEARCH ARTICLE

Spectral method for multidimensional Volterra integral equation with regular kernel

  • Yunxia WEI 1 ,
  • Yanping CHEN , 2 ,
  • Xiulian SHI 3 ,
  • Yuanyuan ZHANG 4
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  • 1. Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, China
  • 2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • 3. School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China
  • 4. Department of Mathematics and Information Science, Yantai University, Yantai 264005, China

Received date: 16 Aug 2016

Accepted date: 22 Feb 2019

Published date: 15 Apr 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

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)=Πi=1d(1xi)α(1+xi)β,1<α,β<1d12 (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.

Cite this article

Yunxia WEI , Yanping CHEN , Xiulian SHI , Yuanyuan ZHANG . Spectral method for multidimensional Volterra integral equation with regular kernel[J]. Frontiers of Mathematics in China, 2019 , 14(2) : 435 -448 . DOI: 10.1007/s11464-019-0758-8

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