A New Approach for Solving Partial Differential Equations in Large Domains using Radial Basis Functions

In this paper, a stable method is proposed for solving time dependent partial differential equations in large domains using radial basis functions. In this new approach, a domain decomposition scheme is applied by using collocation points and thin plate splines. The scheme works in a similar fashion as finite difference methods. The merit of the proposed approach is that it is capable to reduce condition number of the matrices resulting from discretization of the equations and easily overcome the difficulty arising in solving complicated algebraic systems. The new method is applied to linear hyperbolic telegraph and nonlinear Klein-Gordon equations and the obtained results confirm the accuracy and efficiency of this method. The results of numerical experiments are presented with and without using domain decomposition method.