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 language | English |
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Pages (from-to) | 1065-1078 |
Number of pages | 14 |
Journal | Computational Mathematics and Mathematical Physics |
Volume | 36 |
Issue number | 8 |
Publication status | Published - 1996 |