The difference method for the solution of singular perturbation problems for elliptic-parabolic differential equations (Q1084842)

The difference method for the solution of singular perturbation problems for elliptic equations involving a small parameter \(\epsilon\) in the higher derivatives is discussed. As \(\epsilon =0\) the original equations are degenerated into parabolic equations. The authors construct a special difference scheme by means of boundary layer properties of the solutions of these problems as well as investigate the convergence of this scheme and the asymptotic behaviour of solutions. Finally, a numerical example is given.