A Numerical Algorithm for Solving an Inverse Nonlinear Parabolic Problem

Abstract

In this paper, we propose an algorithm for numerical solving an inverse nonlinear diffusion problem. The algorithm is based on the Laplace transform technique and the finite difference method in conjunction with the least-squares scheme. To regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization method to obtain the stable numerical approximation to the solution. To show the efficiency and accuracy of the present method a test problem will be studied.