Numerical solution of an inverse reaction–diffusion problem via collocation method based on radial basis functions

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. This method is a combination of collocation method and radial basis functions. The operational matrix of derivative for radial basis functions 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.