Adv. Appl. Math. Mech., 9 (2017), pp. 1225-1249.
Published online: 2018-05
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1085}, url = {http://global-sci.org/intro/article_detail/aamm/12198.html} }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.