BVPs on infinite intervals: A test problem,a nonstandard finite difference scheme and a posteriori error estimator |
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Authors: | Riccardo Fazio Alessandra Jannelli |
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Affiliation: | Department of Mathematics and Computer Science, Physical Sciences and Earth Sciences, University of Messina, Messina, Italy |
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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. |
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Keywords: | boundary value problems global error estimator nonstandard finite difference order of accuracy quasi‐uniform grid |
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