A Meshfree Approach Based on Moving Kriging Interpolation for Numerical Solution of Coupled Reaction-Diffusion Problems

Abstract

In this paper, a meshfree approach based on moving kriging interpolation is presented for numerical solution of coupled reaction-diffusion problems. The proposed approach is developed based upon local collocation using moving Kriging shape function. It is truly meshless and having the Kronecker delta property for accurate imposition of boundary conditions. In the proposed model, the weight function is used with correlation parameter treated as the model internal length factor. This produces a local moving kriging method with improved accuracy together with an ease to choose the weight function factor. The method can hence be used in an efficient manner without cumbersome effort for choosing its parameter. The meshless approach is presented for the first time for numerical solution of reaction-diffusion systems. Problems of Turing system and pattern formation in several 2D domains are solved in this study. The efficacy and accuracy of the proposed method for the reaction-diffusion systems in different problem domains are presented in comparison to available exact solution and other numerical methods. It is found that the present method is accurate and effective as a computational procedure for solving reaction-diffusion problems.