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- Title
BVPs on infinite intervals: A test problem, a nonstandard finite difference scheme and a posteriori error estimator.
- Authors
Fazio, Riccardo; Jannelli, Alessandra
- Abstract
As far as the numerical solution of boundary value problems defined on an infinite interval is concerned, in this paper, we present a test problem for which the exact solution is known. Then we study an a posteriori estimator for the global error of a nonstandard finite difference scheme previously introduced by the authors. In particular, we show how Richardson extrapolation can be used to improve the numerical solution using the order of accuracy and numerical solutions from 2 nested quasi-uniform grids. We observe that if the grids are sufficiently fine, the Richardson error estimate gives an upper bound of the global error.
- Subjects
NUMERICAL solutions to equations; BOUNDARY value problems; ERROR functions; MATHEMATICAL models; RICHARDSON extrapolation
- Publication
Mathematical Methods in the Applied Sciences, 2017, Vol 40, Issue 18, p6285
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.4456