Numerical implementations of dynamical probe method for non-stationary heat equation

The dynamical probe method for non-stationary heat equation is developed recently, which aims to detect an unknown inclusion of conductive material from the boundary measurement data. The Runge approximation is used to define some indicator function for this method, which is a mathematical testing machine to detect the inclusion. A numerical realization of the Runge approximation is the key to this method. By using a regularizing method, a realization scheme is given for the Runge approximation, and numerical examples are given to show the validity of the dynamical probe method.