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nonstandard finite difference scheme
Nonstandard finite difference schemes is a general set of methods in numerical analysis that gives numerical solutions to differential equations by constructing a discrete model. The general rules for such schemes are not precisely known. 〔 JB Cole, High Accuracy Yee Algorithm Based on Nonstandard Finite Differences: New Developments and Verifications, IEEE Trans. on Antennas and Propagation, vol. 50, no. 9, pp. 1185-1191 (2002)〕
==Overview==
A finite difference (FD) model of a differential equation (DE) can be formed by simply replacing the derivatives with FD approximations. But this is a naive "translation." If
we literally translate from English to Japanese by making a one-to-one correspondence between words, the original meaning is often lost. Similarly the naive FD model of a DE can be very different from the original DE, because the FD model is a difference equation with solutions that may be quite different from solutions of the DE. For a more technical definition see Mickens 2000.〔
A nonstandard (NS) finite difference model, is a free and more accurate "translation" of a differential equation. For example, a parameter (call it ''v'') in the DE may take another value ''u'' in the NS-FD model.
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