Compact filtering as a regularization technique for a backward heat conduction problem

Abstract

In this paper, the backward heat conduction problem is solved numerically using a fourth-order compact difference scheme. For the regularization of this ill-posed problem, fourth-order compact filtering which is a spatial filtering technique is proposed. The second derivative approximation in compact difference scheme has been compared with the fourth-order standard finite difference scheme via Fourier analysis. The comparison shows that the resolution ability of the compact difference scheme is better than the standard finite difference scheme. Meanwhile, an error estimate between the exact and regularized solution is derived. Numerical results are provided using the proposed method. The comparison of CPU time shows that the fourth-order compact difference scheme takes lesser CPU time than the fourth-order standard finite difference scheme.