Artificial boundary conditions for diffusion equations: Numerical study

Recently in [3], a new method has been presented providing a family of artificial boundary conditions for parabolic equations which are local in time and stable. This method applies to variable coefficients and curved boundaries but unfortunately there are no error estimates. As an alternative, we present in this paper numerical simulations showing the efficiency of the method. The construction of the artificial boundary conditions depends on the number and values of points at which z12 is interpolated by rational fractions in the complex plane. Particular attention is paid to the choice of those points.