Geodesic
A two-grid method for a~nonlinear singular perturbation boundary value problem on the Shishkin scheme
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 42-55

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Unders consideration is some boundary value problem for a second order nonlinear singular perturbation ordinary differential equationd. An upwind scheme on the Shishkin mesh is applied. We use the Newton and Picard methods to resolve the difference schemeare investigated. To decrease number of arithmetical operations we use the two-grid method. Application of the Richardson extrapolation is shown to give almost second order accuracy of the difference scheme. The results of some numerical experiments are discussed.
Keywords: nonlinear differential equation, Shishkin mesh, difference scheme, iterative method, two-grid method, Richardson extrapolation.
Mots-clés : singular perturbation 
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     author = {A. I. Zadorin and S. V. Tikhovskaya},
     title = {A two-grid method for a~nonlinear singular perturbation boundary value problem on the {Shishkin} scheme},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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A. I. Zadorin; S. V. Tikhovskaya. A two-grid method for a~nonlinear singular perturbation boundary value problem on the Shishkin scheme. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 42-55. http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a4/