A Domain Decomposition Chebyshev Spectral Collocation Method for Volterra Integral Equations

Authors

  • Hua Wu Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China
  • Yunzhen Zhu Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China
  • Hailu Wang Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China
  • Lingfang Xu Department of Mathematics, Shanghai University, Shanghai 200444, P.R. China

DOI:

https://doi.org/10.4208/jms.v51n1.18.04

Keywords:

Nonlinear Volterra integral equations, domain decomposition method, Chebyshev–collocation spectral method, convergence analysis.

Abstract

We develop a domain decomposition Chebyshev spectral collocation method for the second-kind linear and nonlinear Volterra integral equations with smooth kernel functions. The method is easy to implement and possesses high accuracy. In the convergence analysis, we derive the spectral convergence order under the $L^∞$-norm without the Chebyshev weight function, and we also show numerical examples which coincide with the theoretical analysis.

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Published

2019-01-07

Issue

Vol. 51 No. 1 (2018)

Section

Articles