Spectral method for multidimensional Volterra integral equation with regular kernel

Abstract

This paper is concerned with obtaining an approximate solution for a linear multidimensional Volterra integral equation with a regular kernel. We choose the Gauss points associated with the multidimensional Jacobi weight function (d denotes the space dimensions) as the collocation points. We demonstrate that the errors of approximate solution decay exponentially. Numerical results are presented to demonstrate the eectiveness of the Jacobi spectral collocation method.

Keywords

Multidimensional Volterra integral equation / Jacobi collocation discretization / multidimensional Gauss quadrature formula

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