A study of difference schemes with the first derivative approximated by a central difference ratio

V. B. Andreyev, N. V. Kopteva

Research output: Contribution to journalArticlepeer-review

Abstract

For an ordinary second-order differential equation in which the coefficient of the highest derivative is a small parameter, the classical difference scheme which uses a central difference ratio to approximate the first derivative is investigated. By means of a detailed analysis of Green's function of the grid problem, it is established that the scheme is solvable on Shishkin's piecewise-uniform grid which clusters in the boundary layer and has uniform accuracy O(N-2 In2 N) with respect to the small parameter, where N is the number of grid nodes.

Original languageEnglish
Pages (from-to)1065-1078
Number of pages14
JournalComputational Mathematics and Mathematical Physics
Volume36
Issue number8
Publication statusPublished - 1996

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