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On supraconvergence phenomenon for second order centered finite differences on non-uniform grids

By Gayaz Khakimzyanov and Denys Dutykh

Abstract

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. 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. This example is quite pedagogical and may give some ideas for more complex problems.Comment: 26 pages, 2 figures, 2 tables, 37 references. Other author's papers can be downloaded at http://www.denys-dutykh.com

Topics: Mathematics - Numerical Analysis, Mathematics - Classical Analysis and ODEs, Physics - Classical Physics, Physics - Computational Physics
Publisher: 'Elsevier BV'
Year: 2017
DOI identifier: 10.1016/j.cam.2017.05.006
OAI identifier: oai:arXiv.org:1511.02770

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