Radial basis functions method for solving of a non-local boundary value problem with Neumann’s boundary conditions

In this paper, the problem of solving the two-dimensional diffusion equation subject to a non-local condition involving a double integral in a rectangular region is considered. The solution of this type of problems are complicated. Therefore, a simple meshless method using the radial basis functions is constructed for the non-local boundary value problem with Neumann’s boundary conditions. Numerical examples are included to demonstrate the reliability and efficiency of this method. Also N_e and root mean square errors are obtained to show the convergence of the method.