THE USE OF INVERSE QUADRATIC RADIAL BASIS FUNCTIONS FOR THE SOLUTION OF AN INVERSE HEAT PROBLEM

In this paper, a numerical procedure for an inverse problem of simultaneously determining an unknown coefficient in a semilinear parabolic equation subject to the specification of the solution at an internal point along with the usual initial boundary conditions is considered. The method consists of expanding the required approximate solution as the elements of the inverse quadratic radial basis functions (IQ-RBFs). The operational matrix of derivative for IQ-RBFs is introduced and the new computational technique is used for this purpose. The operational matrix of derivative is utilized to reduce the problem to a set of algebraic equations. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results.