A real distinct poles Exponential Time Differencing scheme for reaction–diffusion systems

A second order Exponential Time Differencing (ETD) method for reaction–diffusion systems which uses a real distinct poles discretization method for the underlying matrix exponentials is developed. The method is established to be stable and second order convergent. It is demonstrated to be robust for...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-06, Vol.299, p.24-34
Main Authors: Asante-Asamani, E.O., Khaliq, A.Q.M., Wade, B.A.
Format: Article
Language:English
Subjects:
Boundary conditions
Computation
Discretization
Exponential Time Differencing
Mathematical analysis
Mathematical models
Poles
Reaction–diffusion equations
Semilinear parabolic problems
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Summary:A second order Exponential Time Differencing (ETD) method for reaction–diffusion systems which uses a real distinct poles discretization method for the underlying matrix exponentials is developed. The method is established to be stable and second order convergent. It is demonstrated to be robust for problems involving non-smooth initial and boundary conditions and steep solution gradients. We discuss several advantages over competing second order ETD schemes.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.09.017