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Stable Rotational Symmetric Schemes for Nonlinear Reaction-diffusion Equations by Philku Lee; George V. Popescu; Seongjai Kim is a Engineering article available to read on EtoBox.

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## Reaction-diffusion equations Biological pattern formation Time-stepping procedure Variable-θ method Rotational symmetry Averaging scheme In the simulation of biological pattern forming, it has been observed that the numerical solution is more sensitive to the spatial mesh resolution than the temporal one. Such a higher sensitivity to the spatial resolution is mainly originated from an inaccurate approximation of diffusion differential operators, which might violate the rotational symmetry to be seriously erroneous in low spatial resolutions. Also, it has been known that the second-order Crank-Nicolson time-stepping procedure may introduce spurious oscillations when the initial data or the source term is nonsmooth and the temporal step size is set relatively large. This article studies 9-point finite difference schemes for the diffusion operator to enhance the rotational symmetry, employs the variable-θ method to achieve a nonoscillatory second-order time-stepping procedure, and adopts an effective relaxation linear solver to solve the algebraic systems efficiently. The variable-θ method is proved to satisfy the maximum principle, which guarantees that the time-stepping procedure

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Author

Philku Lee; George V. Popescu; Seongjai Kim

Publisher

Elsevier BV

Published

2022

Language

EN

Field

Engineering (Physical Sciences)