A pseudospectral scheme and its convergence analysis for high-order integro-differential equations

Abstract

The main purpose of this work is to develop an integral pseudospectral scheme for solving integro-differential equations. We provide new pseudospectral integration matrices (PIMs) for the Legendre–Gauss and the flipped Legendre–Gauss–Radau points, respectively, and present an efficient and stable approach to computing the PIMs via the recursive calculation of Legendre integration matrices. Furthermore, we provide a rigorous convergence analysis for the proposed pseudospectral scheme in both L∞ and L2 spaces via a linear integral equation, and the spectral rate of convergence is demonstrated by numerical results.