@Article{AAMM-9-1225,
author = {Jannesari , Zahra and Tatari , Mehdi},
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 = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2015.m1085},
url = {http://global-sci.org/intro/article_detail/aamm/12198.html}
}