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A Multistep Legendre Pseudo-Spectral Method for Nonlinear Volterra Integral Equations

  • Zhang Xiao-Yong and Li Jun-Lin EMAIL logo
Published/Copyright: September 18, 2019

Abstract

In this paper, we extend the single-step pseudo-spectral method for nonlinear Volterra integral equations of the second kind to the multistep pseudo-spectral method. We also analyze the convergence of the hp-version of the multistep pseudo-spectral method under the L2-norm, and the result shows that the scheme enjoys high order accuracy and can be implemented in a stable and efficient manner. In addition, it is very suitable for long time calculations and large step size situations. Numerical experiments confirm the theoretical expectations.

MSC 2010: 45D05; 45G10; 41A10; 65L60; 65L70

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Received: 2018-02-17
Accepted: 2019-01-12
Published Online: 2019-09-18
Published in Print: 2020-02-25

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