Институт вычислительной математики
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Тезисы докладов

Численное решение дифференциальных и интегральных уравнений

documentstyle[12pt]{article} title{Robust numerical method for a singularly perturbed equation with unboundedly growing convective term at infinity} author{Aliona I. Dreglea, Grigori I. Shishkin} date{} begin{document} maketitle

Diriclet's problem for a singularly perturbed ordinary differential convection-diffusion equation is considered. The convective term grows at infinity as $O(x)$. Two characteristic scales are observed for this problem on the semiaxis, i.e., regular and boundary layer scales that are controlled by the data of the reduced problem and by the perturbation parameter $epsilon$. For finite $epsilon$, such a problem models Blasius' problem arising in the study of self-similar flow of viscous incompressible liquid. Using special meshes condensing in the boundary layer, we construct schemes on meshes with finite and infinite numbers of nodes whose solutions are $epsilon$-uniformly convergent on the semiaxis.

Acknowledgements. This work was supported by the Russian Foundation for Basic Research under grant No. 04-01-00578. end{document}

Примечание. Тезисы докладов публикуются в авторской редакции

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