UNIFORM DIFFERENCE SCHEME FOR HYPERBOLIC-HYPERBOLIC SINGULAR PERTURBATION MIXED PROBLEMS

A difference scheme is established in this paper for second-order hyperbolic-hyperbolicsingular perturbation mixed problems. We give an energy inequality of the numericalsolution and prove that the numerical solution converges to the solution of the singularperturbation problems uniformly with respect to a small parameter and in the sense of adiscrete norm.