The use of radial basis functions for the solution of a partial differential equation with an unknown time-dependent coefficient

Abstract

In this paper, a numerical technique is presented for the solution of a parabolic partial differential equation with a time-dependent coefficient subject to an extra measurement. For solving the discussed inverse problem, at first we transform it into a nonlinear direct problem and then use the proposed method. This method is a combination of collocation method and radial basis functions. The radial basis functions (RBFs) method is an efficient meshfree technique for the numerical solution of partial differential equations. The main advantage of numerical methods which use radial basis functions over traditional techniques is the meshless property of these methods. The accuracy of the method is tested in terms of maximum and RMS errors. Illustrative examples are included to demonstrate the validity and applicability of the technique.