Abstract
Numerical methods are considered for singularly perturbed quasilinear problems having interior-shock solutions. It is shown that the direct discretization on a layer-adapted mesh is ineffective for these problems. A special method is proposed for the case when the solution is monotonic: the problem is transformed by interchanging the dependent and independent variables, and it is then discretized on a uniform mesh. The method is analyzed both theoretically and numerically. It is shown that it can be effective, but that it is not entirely without problems. An approach for improving the method is suggested.
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