Achieving Very High Order for Implicit Explicit Time Stepping: Extrapolation Methods

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TR Number

TR-08-13

Date

2008-07-01

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Publisher

Department of Computer Science, Virginia Polytechnic Institute & State University

Abstract

In this paper we construct extrapolated implicit-explicit time stepping methods that allow to efficiently solve problems with both stiff and non-stiff components. The proposed methods can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method of lines framework. These methods are simple to construct, easy to implement and parallelize. We establish the existence of perturbed asymptotic expansions of global errors, explain the convergence orders of these methods, and explore their linear stability properties. Numerical results with stiff ODEs, DAEs, and PDEs illustrate the theoretical findings and the potential of these methods to solve multiphysics multiscale problems.

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Keywords

Numerical analysis

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