Numerical solution to a sideways parabolic equation

The inverse heat conduction problem can be considered to be a sideways parabolic equation in the quarter plane. This is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but one side is inaccessible to measurements. A numerical procedure for this severely ill-posed problem is suggested, which consists of two steps, namely a molli cation of the data and a marching di erence scheme. The numerical method is proved to be stable. Several computational results are presented and discussed