A Meshfree Technique for Numerical Simulation of Reaction-Diffusion Systems in Developmental Biology
Year: 2017
Author: Zahra Jannesari, Mehdi Tatari
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 5 : pp. 1225–1249
Abstract
In this work, element free Galerkin (EFG) method is posed for solving nonlinear, reaction-diffusion systems which are often employed in mathematical modeling in developmental biology. A predictor-corrector scheme is applied, to avoid directly solving coupled nonlinear systems. The EFG method employs the moving least squares (MLS) approximation to construct shape functions. This method uses only a set of nodal points and a geometrical description of the body to discretize the governing equation. No mesh in the classical sense is needed. However, a background mesh is used for integration purpose. Numerical solutions for two cases of interest, the Schnakenberg model and the Gierer-Meinhardt model, in various regions are presented to demonstrate the effects of various domain geometries on the resulting biological patterns.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2015.m1085
Advances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 5 : pp. 1225–1249
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Element free Galerkin (EFG) method reaction-diffusion systems meshfree methods MLS approximation developmental biology.