Summary
We present a modified first-order backward Euler finite difference scheme to solve advection-reaction-diffusion systems on fixed and continuously deforming domains. We compare our scheme to the second-order semi-implicit backward finite differentiation formula and conclude that for the type of equations considered, the first-order scheme has a larger region of stability for the time step than that of the second-order scheme (at least by a factor of ten) and therefore the first-order scheme becomes a natural choice when solving advection-reactiondiffusion systems on growing domains.
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Madzvamuse, A. (2007). A Modified Backward Euler Scheme for Advection-Reaction-Diffusion Systems. In: Deutsch, A., Brusch, L., Byrne, H., Vries, G.d., Herzel, H. (eds) Mathematical Modeling of Biological Systems, Volume I. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4558-8_16
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DOI: https://doi.org/10.1007/978-0-8176-4558-8_16
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4557-1
Online ISBN: 978-0-8176-4558-8
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