Boundary Shock Problems and Singularly Perturbed Riccati Equations

摘要

A quasilinear singularly perturbed boundary-value problem is considered under conditions which guarantee that the solution has a boundary shock. The problem is initially transformed to a Riccati initial-value problem which is then solved numerically using the backward Euler scheme on a Shishkin-type mesh. For this method, a robust error estimate is proved and illustrated by numerical experiments.