Smooth solution of partial integro-differential equations using radial basis functions

In this work, we present the method based on radial basis functions to solve partial integro-differential equations. We focus on the parabolic type of integro-differential equations as the most common forms including the ``\emph{memory}'' of the systems. We propose to apply the collocation scheme using radial basis functions to approximate the solutions of partial integro-differential equations. Due to the presented technique, system of linear or nonlinear equations is made instead of primary problem. The method is efficient because the rate of convergence of collocation method based on radial basis functions is exponential. Some numerical examples and investigation of the experimental results show the applicability and accuracy of the method.