Spectral discretizations analysis with time strong stability preserving properties for pseudo-parabolic models

Abstract

In this work, we study the numerical approximation of the initial-boundary-value problem of nonlinear pseudo-parabolic equations with Dirichlet boundary conditions. We propose a discretization in space with spectral schemes based on Jacobi polynomials and in time with robust schemes attending to qualitative features such as stiffness and preservation of strong stability for a more correct simulation of non-regular data. Error estimates for the corresponding semidiscrete Galerkin and collocation schemes are derived. The performance of the fully discrete methods is analyzed in a computational study.