Fully pseudospectral time evolution and its application to 1+1 dimensional physical problems

TL;DR

This paper demonstrates that a fully pseudospectral time evolution method, previously applied to simple wave equations, can be effectively extended to complex nonlinear PDE systems in astrophysics and cosmology.

Contribution

It introduces the application of fully pseudospectral schemes to nonlinear PDEs in physical problems like stellar oscillations and cosmological models, expanding the method's scope.

Findings

Successfully applied to radial oscillations of Newtonian stars

Extended to time evolution of Gowdy spacetimes

Showed the method's effectiveness for nonlinear PDE systems

Abstract

It was recently demonstrated that time-dependent PDE problems can numerically be solved with a fully pseudospectral scheme, i.e. using spectral expansions with respect to both spatial and time directions (Hennig and Ansorg, 2009 [15]). This was done with the example of simple scalar wave equations in Minkowski spacetime. Here we show that the method can be used to study interesting physical problems that are described by systems of nonlinear PDEs. To this end we consider two 1+1 dimensional problems: radial oscillations of spherically symmetric Newtonian stars and time evolution of Gowdy spacetimes as particular cosmological models in general relativity.