Monte Carlo simulation via a numerical algorithm for solving a nonlinear inverse problem

This paper is intended to provide a numerical algorithm involving the combined use of the finite differences scheme and Monte Carlo method for estimating the diffusion coefficient in a one-dimensional nonlinear parabolic inverse problem. In the present study, the functional form of the diffusion coefficient is unknown a priori. The unknown diffusion coefficient is approximated by the polynomial form and the present numerical algorithm is employed to find the solution. To modify the values of estimated coefficients of this polynomial form, we introduce a random search algorithm in Monte Carlo method for global optimization. A numerical test is performed in order to show the efficiency and accuracy of the present work.