AN INTRODUCTION TO NONSTANDARD FINITE DIFFERENCE SCHEMES
1999 ◽
Vol 07
(01)
◽
pp. 39-58
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Keyword(s):
Nonstandard finite difference schemes offer the potential for either constructing exact discrete models of differential equations or obtaining discrete models that do not have the elementary numerical instabilities. While the general laws for constructing such schemes are not precisely known at the present time, a number of important rules have been discovered. This paper provides an introduction to the nonstandard finite difference rules, explains their significance, and applies them to several model ordinary and partial differential equations. Several major unresolved issues and problems are briefly discussed.
2001 ◽
Vol 77
(1)
◽
pp. 135-144
◽
2014 ◽
Vol 94
(11)
◽
pp. 974-974
2011 ◽
Vol 179
(1)
◽
pp. 100-126
◽
2016 ◽
Vol 54
(1)
◽
pp. 86-119
◽
2010 ◽
Vol 42
(5)
◽
pp. 2275-2296
◽
2009 ◽