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 Ne and root mean square errors are obtained to show the convergence of the method.