Uniform difference scheme for hyperbolic-hyperbolic singular perturbation mixed problems
A difference scheme for a second order hyperbolic-hyperbolic singular perturbation mixed problem with a small parameter \(\epsilon >0\) for the equation \(\epsilon (u_{xx}-u_{tt})=u_ t+au_ x+f(t,x)\) is established. An energy inequality for the numerical solution is given and it is proved that the numerical solution converges to the solution of the singular perturbation problems uniformly with respect to the small parameter and in the sense of a discrete norm. In a numerical example the difference solution and the asymptotic solution are compared.
second order hyperbolic- hyperbolic singular perturbation mixed problem
scientific article; zbMATH DE number 4026718