An $hp$-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels

Abstract

This paper presents an $hp$-version Chebyshev spectral collocation method for nonlinear Volterra integro-differential equations with weakly singular kernels. The $hp$-version error bound of the collocation method under the $H$¹-norm is established on an arbitrary mesh. Numerical experiments demonstrate the effectiveness of the proposed method.