Volume 9, Issue 5
A Meshfree Technique for Numerical Simulation of Reaction-Diffusion Systems in Developmental Biology

Zahra Jannesari & Mehdi Tatari

Adv. Appl. Math. Mech., 9 (2017), pp. 1225-1249.

Published online: 2018-05

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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) method, reaction-diffusion systems, meshfree methods, MLS approximation, developmental biology.

  • AMS Subject Headings

65M99, 92B99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-1225, author = {}, title = {A Meshfree Technique for Numerical Simulation of Reaction-Diffusion Systems in Developmental Biology}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {5}, pages = {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 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1085}, url = {http://global-sci.org/intro/article_detail/aamm/12198.html} }
TY - JOUR T1 - A Meshfree Technique for Numerical Simulation of Reaction-Diffusion Systems in Developmental Biology JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1225 EP - 1249 PY - 2018 DA - 2018/05 SN - 9 DO - http://dor.org/10.4208/aamm.2015.m1085 UR - https://global-sci.org/intro/article_detail/aamm/12198.html KW - Element free Galerkin (EFG) method, reaction-diffusion systems, meshfree methods, MLS approximation, developmental biology. AB -

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.

Zahra Jannesari & Mehdi Tatari. (2020). A Meshfree Technique for Numerical Simulation of Reaction-Diffusion Systems in Developmental Biology. Advances in Applied Mathematics and Mechanics. 9 (5). 1225-1249. doi:10.4208/aamm.2015.m1085
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