Error estimates for semidiscrete Galerkin and collocation approximations to pseudo-parabolic problems with Dirichlet conditions

TL;DR

This paper derives error estimates for spectral Galerkin and collocation methods using Jacobi polynomials applied to nonlinear pseudo-parabolic equations with Dirichlet boundary conditions.

Contribution

It provides the first rigorous error analysis for spectral Galerkin and collocation schemes on this class of nonlinear pseudo-parabolic problems.

Findings

Error bounds for Galerkin schemes established

Error bounds for collocation schemes established

Spectral methods show high accuracy for these problems

Abstract

This paper is concerned with the numerical approximation of the Dirichlet initial-boundary-value problem of nonlinear pseudo-parabolic equations with spectral methods. Error estimates for the semidiscrete Galerkin and collocation schemes based on Jacobi polynomials are derived.