A Chebyshev Spectral Collocation Method for Nonlinear Volterra Integral Equations with Vanishing Delays

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Abstract

A multistep Chebyshev-Gauss-Lobatto spectral collocation method for nonlinear Volterra integral equations with vanishing delays is developed. The convergence of the hp-version of the method in supremum norm is proved. Numerical experiments show the efficiency of the method for equations with highly oscillating, steep gradient and non-smooth solutions.

Keywords:

Multistep Chebyshev-Gauss-Lobatto spectral collocation method nonlinear Volterra integral equation vanishing variable delay.
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DOI

10.4208/eajam.130416.071217a