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 -

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.