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 methods(JSGM,JPSGM) under reasonable assumptions, which indicate that the approximate solution errors decay exponentially in the sense of L ∞ and L ω 2 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.