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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

##### MSC:
 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