A fourth-order compact difference scheme for the parabolic inverse problem with an overspecification

چکیده مقاله

The problem of finding the s olution of partial differential equation with source control parameter has appeared increasingly i n physical phenomena, f or example, in the s tudy of heat conduction process, chemical diff usion and control t heory. In this paper, we use a high-order s cheme f or determining unknown control parameter and unknown s olution of parabolic inverse problem. I n t he proposed numerical scheme, we r eplace the s pace derivative with a f ourth-order compact finite diff erence approximation. We will investigate t he stability and convergence of proposed scheme and s how that the convergence order i s O (τ 2 + h 4 ). Also due to the usually ill-posed nature of inverse problems, we examine the stability of method with respect to perturbations of the data. Numerical results corroborate the t heoretical results and high accuracy of proposed scheme in comparison with the other methods in the literature.