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High order adaptive methods of Nyström-Cowell type

✍ Scribed by J.M. Franco; J.F. Palacian

Book ID
104338414
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
817 KB
Volume
81
Category
Article
ISSN
0377-0427

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✦ Synopsis

A class of unconditionally stable multistep methods is discussed for solving initial-value problems of second-order differential equations which have periodic or quasiperiodic solutions. This situation frequently occurs in celestial mechanics, in nonlinear oscillations and various other situations. The methods depend upon a parameter co > 0, and integrate exactly trigonometric functions along with algebraic polynomials. In this paper we show a procedure for the construction of adaptive Nystr/Sm-Cowell formulas of arbitrarily high order of accuracy, and reduce to the classical NystriSm-Cowell methods for co = 0. Our methods compare advantageously with other methods.

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