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A second order uniform numerical method for a turning point problem. (English) Zbl 0693.65051
The solution of a second order boundary value problem with a small parameter \(\epsilon\) at the highest derivative is investigated. A non- equidistant generalization of the Gushchin-Shchennikov scheme is used on a constructed special discretization mesh. Stability uniform in \(\epsilon\) and second order accuracy are obtained. Numerical results for the solution of a test problem for given \(\epsilon\) are presented in a table.
Reviewer: I.N.Molchanov

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
34E15 Singular perturbations, general theory for ordinary differential equations