A fourth-order exponential time differencing scheme with dimensional splitting for non-linear reaction-diffusion systems

arXiv (Cornell University)

Abstract

A fourth-order exponential time differencing (ETD) Runge-Kutta scheme with dimensional splitting is developed to solve multidimensional non-linear systems of reaction-diffusion equations (RDE). By approximating the matrix exponential in the scheme with the A-acceptable Padé (2,2) rational function, the resulting scheme (ETDRK4P22-IF) is verified empirically to be fourth-order accurate for several RDE. The scheme is shown to be more efficient than competing fourth-order ETD and IMEX schemes, achieving up to 20 times speed in CPU time. Inclusion of up to three pre-smoothing steps of a lower order L-stable scheme facilitates efficient damping of spurious oscillations arising from problems with non-smooth initial/boundary conditions.

Authors 3

1. Emmanuel Owusu Asante-Asamani

   Clarkson University

   Affiliation as printed

   Department of Mathematics , Clarkson University Potsdam NY 13676 , USA

2. Andreas Kleefeld Aachen Faculty of Medical Engineering and Technomathematics

   FH Aachen · Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Faculty of Medical Engineering and Technomathematics , University of Applied Sciences Aachen , 52428 Jülich , Germany

   Jülich Supercomputing Centre , Forschungszentrum Jülich GmbH , 52425 Jülich , Germany

3. Bruce A. Wade

   University of Louisiana at Lafayette

   Affiliation as printed

   Department of Mathematics , University of Louisiana at Lafayette , Lafayette LA 70504 , USA