A discrete eigenfunctions method for computing mixed hyperbolic problems based on an implicit difference scheme

摘要

In this paper numerical solutions of mixed hyperbolic problems are computed using a discrete eigenfunctions method combined with an implicit difference scheme. This new numerical technique preserves the qualitative properties of the analytic solution due to the Sturm–Liouville structure of the underlying discrete linear boundary-value problem and has computational stability advantages vs other methods. Illustrative examples are included.