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A Meshfree Technique for Numerical Simulation of Reaction-Diffusion Systems in Developmental Biology

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Mathematical biology in general

Published online by Cambridge University Press:  11 July 2017

Zahra Jannesari  and
Mehdi Tatari
Zahra Jannesari*
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran
Mehdi Tatari*
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran
*
*Corresponding author. Email:z.jannesari@math.iut.ac.ir (Z. Jannesari), mtatari@cc.iut.ac.ir (M. Tatari)
*Corresponding author. Email:z.jannesari@math.iut.ac.ir (Z. Jannesari), mtatari@cc.iut.ac.ir (M. Tatari)
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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 predicator-corrector scheme is applied, to avoid directly solving of 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 is presented to demonstrate the effects of various domain geometries on the resulting biological patterns.

Keywords

Element free Galerkin (EFG) methodreaction-diffusion systemsmeshfree methodsMLS approximationdevelopmental biology

MSC classification

Secondary: 65M99: None of the above, but in this section 92B99: None of the above, but in this section
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 5 , October 2017 , pp. 1225 - 1249
Copyright
Copyright © Global-Science Press 2017 

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