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An Exponential Time Differencing Scheme With A Real Distinct Poles Rational Function For Advection-Diffusion Reaction Equations, Emmanuel Owusu Asante-Asamani

Theses and Dissertations

A second order Exponential Time Differencing (ETD) scheme for advection-diffusion reaction systems is developed by using a real distinct poles rational function for approximating the underlying matrix exponential. The scheme is proved to be second order convergent. It is demonstrated to be robust for reaction-diffusion systems with non-smooth initial and boundary conditions, sharp solution gradients, and stiff reaction terms. In order to apply the scheme efficiently to higher dimensional problems, a dimensional splitting technique is also developed. This technique can be applied to all ETD schemes and has been found, in the test problems considered, to reduce computational time by …