Analysis of difference schemes for a stationary shock problem. (English) Zbl 0574.65103

We consider the limit function U of the solutions \(u_{\epsilon}\) of a singularly perturbed boundary value problem. In general, U will be discontinuous. Two difference approximations of the boundary value problem are studied and the discrete values for \(\epsilon =0\), \(h\to 0\) are compared with U. Error estimates of order O(h) and \(O(h^ 2)\) are proved and the sharpness of numerical layers is established.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
76L05 Shock waves and blast waves in fluid mechanics
34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
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