Geodesic
Solution of second order nonlinear singular perturbation ordinary differential equation based on the Samarskii scheme
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 1, pp. 11-25

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A boundary value problem for a second order nonlinear singular perturbation ordinary differential equation is considered. We propose the method based on the Newton and the Picard linearizations using known modified Samarskii scheme on the Shishkin mesh in the case of a linear problem. It is proved that the constructed difference schemes are of second order and uniformly convergent. To decrease the number of the arithmetical operations, we propose a two-grid method. The results of some numerical experiments are discussed. 
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     author = {A. I. Zadorin and S. V. Tikhovskaya},
     title = {Solution of second order nonlinear singular perturbation ordinary differential equation based on the {Samarskii} scheme},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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     publisher = {mathdoc},
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A. I. Zadorin; S. V. Tikhovskaya. Solution of second order nonlinear singular perturbation ordinary differential equation based on the Samarskii scheme. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 16 (2013) no. 1, pp. 11-25. http://geodesic.mathdoc.fr/item/SJVM_2013_16_1_a1/