Solving 2D Reaction-Diffusion Equations with Nonlocal Boundary Conditions by the RBF-MLPG Method

Abstract

This paper is concerned with the development of a new approach for the numerical solution of linear and nonlinear reaction-diffusion equations in two spatial dimensions with Bitsadze-Samarskii type nonlocal boundary conditions. Proper finite-difference approximations are utilized to discretize the time variable. Then, the weak equations of resultant elliptic type PDEs are constructed on local subdomains. These local weak equations are discretized by using the multiquadric (MQ) radial basis function (RBF) approximation where an iterative procedure is proposed to treat the nonlinear terms in each time step. Numerical test problems are given to verify the accuracy of the obtained numerical approximations and stability of the proposed method versus the parameters of the nonlocal boundary conditions.