Finding timewise diffusion coefficient from nonlocal integral condition in one-dimensional heat equation

The problem of numerical identification for thermal diffusivity in one-dimension heat equation has been considered. Under non-linear nonlocal over determination condition the problem investigated. This conditions guarantees the unique solvability of the solution. Based on finite difference scheme the forward problem sought via Crank-Nicolson regime is discretized. On the other side, inverse direction viewed as finding quasi-solution for least squares minimization problem. This accomplished using the built-in routine lsqnonlin from the MATLAB optimization toolbox. Two test examples are presented and thoughtfully Analysed via root mean squares error (rmse). The numerically inverted function are stable even with inclusion of various noise levels. We obtain very good result without need of regularization.