Geodesic
On a first-order accurate difference scheme for a singularly perturbed problem with a turning point
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 120-135 Cet article a éte moissonné depuis la source Math-Net.Ru

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A singularly perturbed problem with a turning point is considered. The solution has a boundary layer of exponential type in a neighborhood of a boundary point. The problem is solved approximately by means of a difference scheme of exponential fitting on a uniform grid. It is proved that the solutions obtained from this scheme converge uniformly with respect to the perturbation parameter with the first order of accuracy to the solution of the original differential problem as the grid step tends to zero.
Keywords: singularly perturbed problem for a second-order ordinary differential equation, asymptotic expansion, difference scheme. 
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K. V. Emel'yanov. On a first-order accurate difference scheme for a singularly perturbed problem with a turning point. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 120-135. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a11/

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