Nonstandard Finite Difference Schemes for Differential Equations
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- 1 January 2002
- journal article
- research article
- Published by Taylor & Francis in Journal of Difference Equations and Applications
- Vol. 8 (9) , 823-847
- https://doi.org/10.1080/1023619021000000807
Abstract
This paper gives an introduction to nonstandard finite difference methods useful for the construction of discrete models of differential equations when numerical solutions are required. While the general rules for such schemes are not precisely known at the present time, several important criterion have been found. We provide an explanation of their significance and apply them to several model ordinary and partial differential equations. The paper ends with a discussion of several outstanding problems in this area and other related issues.Keywords
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