Инд. авторы:	Khakimzyanov G., Dutykh D.
Заглавие:	On supraconvergence phenomenon for second order centered finite differences on non-uniform grids
Библ. ссылка:	Khakimzyanov G., Dutykh D. On supraconvergence phenomenon for second order centered finite differences on non-uniform grids // Journal of Computational and Applied Mathematics. - 2017. - Vol.326. - P.1-14. - ISSN 0377-0427. - EISSN 1879-1778.
Внешние системы:	DOI: 10.1016/j.cam.2017.05.006; РИНЦ: 31042963; SCOPUS: 2-s2.0-85019716220; WoS: 000405977300001;
Реферат:	eng: In the present study we consider an example of a boundary value problem for a simple second order ordinary differential equation, which may exhibit a boundary layer phenomenon depending on the value of a free parameter. To this equation we apply an adaptive numerical method on redistributed grids. We show that usual central finite differences, which are second order accurate on a uniform grid, can be substantially upgraded to the fourth order by a suitable choice of the underlying non-uniform grid. Moreover, we show also that some other choices of the nodes distributions lead to substantial degradation of the accuracy. This example is quite pedagogical and we use it only for illustrative purposes. It may serve as a guidance for more complex problems. © 2017 Elsevier B.V.
Ключевые слова:	Supraconvergence; Second-order ordinary differential equations; Non-uniform grids; Finite differences; Complex problems; Central finite difference; Centered finite differences; Adaptive numerical methods; Numerical methods; Finite difference method; Differential equations; Boundary value problems; Supraconvergence; Non-uniform grids; Finite differences; Boundary value problems; Boundary layer; Ordinary differential equations; Boundary layers;
Издано:	2017
Физ. характеристика:	с.1-14
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