TY - JOUR
T1 - A Meshfree Technique for Numerical Simulation of Reaction-Diffusion Systems in Developmental Biology
AU - Jannesari , Zahra
AU - Tatari , Mehdi
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1225
EP - 1249
PY - 2018
DA - 2018/05
SN - 9
DO - http://doi.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 - <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>