Please cite this article as: F. Parzlivand, A.M. Shahrezaee, Numerical solution of an inverse reaction-diffusion problem via collocation method based on radial basis functions, Appl. Math. Modelling (2014), doi: http://dx. 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. 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.

An inverse heat problem of finding an unknown parameter p(t) in the parabolic initial-boundary value problem is solved with variational iteration method (VIM). For solving the discussed inverse problem, at first we transform it into a nonlinear direct problem and then use the proposed method. Also an error analysis is presented for the method and prior and posterior error bounds of the approximate solution are estimated. The main property of the method is in its flexibility and ability to solve nonlinear equation accurately and conveniently. Some examples are given to illustrate the effectiveness and convenience of the method.

This paper uses the collocation method and radial basis functions (RBFs) to analyze the solution of a two-dimension inverse heat conduction problem (IHCP). The accuracy of the method is tested in terms of Error and RMS errors. Also, the stability of the technique is investigated by perturbing the additional specification data by increasing the amounts of random noise. The results of numerical experiments are compared with the analytical solution in illustrative examples to confirm the accuracy and efficiency of the presented scheme.