Legendre spectral Galerkin method for second-kind Volterra integral equations

Abstract

The Legendre spectral Galerkin method for the Volterra integral equations of the second kind is proposed in this paper. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors (in the L₂ norm) will decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical examples are given to illustrate the theoretical results.

Keywords

Volterra integral equation / Legendre spectral Galerkin method / convergence

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