A high accurate and convergent numerical framework for solving high-order nonlinear Volterra integro-differential equations

This article discuss about the application of Jacobi spectral and pseudo-spectral Galerkin techniques for solving high-order nonlinear Volterra integro-differential equations. We supply strict error analysis for Jacobi spectral and pseudo-spectral Galerkin meth-ods(JSGM,JPSGM) under reasonable assumptions, which indicate that the approximate solution errors decay exponentially in the sense of L infinity and L2 omega norm. Some numerical experiments are presented to verify the theoretical results. Superior numerical results with respect to some recent methods are provided in tables and figures.(c) 2022 Elsevier B.V. All rights reserved.