Geodesic
Difference fitting scheme for a singularly perturbed problem with turning point
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 80-91 Cet article a éte moissonné depuis la source Math-Net.Ru

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A singularly perturbed problem with turning point is considered. The solution has two exponential type boundary layers of different orders in neighborhoods of boundary points. 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 to the solution of the original differential problem as the grid step tends to zero.
Keywords: singularly perturbed problem for second-order ordinary differential equation, asymptotic expansion, difference scheme. 
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K. V. Emel'yanov. Difference fitting scheme for a singularly perturbed problem with turning point. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 2, pp. 80-91. http://geodesic.mathdoc.fr/item/TIMM_2012_18_2_a7/

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