Uniform difference scheme for hyperbolic-hyperbolic singular perturbation mixed problems

A difference scheme is established in this paper for second-order hyperbolic-hyperbolic singular perturbation mixed problems. We give an energy inequality of the numerical solution and prove that the numerical solution converges to the solution of the singular perturbation problems uniformly with respect to a small parameter and in the sense of a discrete norm.This paper was read out in the Second National Symposium on Computing Hydromechanics which was held in May of 1984 in Wuxi, Jiangsu, China.