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Lithuanian Mathematical Journal

, Volume 58, Issue 1, pp 75–94 | Cite as

Convergence analysis of the spectral collocation methods for two-dimensional nonlinear weakly singular Volterra integral equations*

  • Xiulian Shi
  • Yunxia Wei
Article
  • 44 Downloads

Abstract

We apply Jacobi spectral collocation approximation to a two-dimensional nonlinear weakly singular Volterra integral equation with smooth solutions. Under reasonable assumptions on the nonlinearity, we carry out complete convergence analysis of the numerical approximation in the L-norm and weighted L2-norm. The provided numerical examples show that the proposed spectral method enjoys spectral accuracy.

Keywords

Volterra integral equations weakly singular kernels Jacobi spectral collocation method convergence analysis 

MSC

45D05 65R20 65M70 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsZhaoqing UniversityZhaoqingChina
  2. 2.Department of MathematicsHangzhou Normal UniversityHangzhouChina

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