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Given a one-step numerical scheme, on which ordinary differential equations is it exact?

✍ Scribed by Francisco R. Villatoro

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 485 KB
Volume: 223
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2008.03.038

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✦ Synopsis

a b s t r a c t

A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's thirdorder rational methods are presented.

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