NUMERICAL INTERFACES IN FINITE DIFFERENCE METHODS FOR HYPERBOLIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS

In this paper, we discuss the interface problems arising in using finite difference methods to solve hyperbolic equations with discontinuous coefficients. The schemes developed here can be used to handle four important types of numerical interfaces due to: (1) the discontinuity of the coefficients of the PDE, (2) using artificial boundary, (3) using different finite difference formulae in different areas, and (4) using different grid sizes in different areas. Stability analysis for these schemes is carried out in terms of conventional l₁, l₂, and l_∞ norms so that the convergence rates of these schemes are obtained. Several numerical examples are supplied to demonstrate properties of these schemes.