A local integral equation formulation to solve coupled nonlinear reaction–diffusion equations by using moving least square approximation

A new procedure is developed for the numerical solution of the nonlinear reaction–diffusion equations responsible for appearance of diffusion driven instabilities. The system of two nonlinear partial differential equations of the parabolic type is proposed to be solved by the local integral equation formulation and one-step time discretization method. The spatial variations are approximated by moving least squares and the nonlinear terms are treated iteratively within each time step. The developed formulation is verified in two numerical test examples with investigating the convergence and accuracy of numerical results.