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Efficient numerical methods for reaction-diffusion problems
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In this book, some time-dependent partial differential equations are considered, and systems of such equations, that governs reaction-diffusion models in biology. It involves the design and implement some novel exponential time differencing schemes to integrate stiff systems of ordinary differential equations which arise from semi-discretization of the associated partial differential equations. We present stability properties of these methods along with extensive numerical simulations for a number of different reaction-diffusion models, including single and multi-species models. When the diffusivity is small many of the models considered in this work are found to exhibit a form of localized spatiotemporal patterns. Such patterns are correctly captured by our proposed numerical schemes. Hence, the schemes that we have designed in this book are dynamically consistent. Finally, in many cases, we have compared our numerical results with those obtained by other researchers.
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