Abstract:In this paper, the inverse heat conduction problem governed by sideways heat equation is investigated numerically. The problem is ill-posed because the solution, if it exists, does not depend continuously on the data. To begin with, this ill-posed problem is analyzed by considering the stability of the semi-discretization numerical schemes. Then the resulting ordinary differential equations at the discretized times are numerically integrated towards the spatial direction by the group preserving scheme, and the stable range of the index$r = 1/2 \nu \Delta t$ is investigated. When the numerical results are compared with exact solutions, it is found that they are in a good agreement even under noisy data. It is also shown that the group preserving scheme is quite effective and better than other numerical solvers, including the fourth-order Runge-Kutta method.