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A note on the efficient implementation of implicit methods for ODEs

โœ Scribed by Pierluigi Amodio; Luigi Brugnano

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
383 KB
Volume
87
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

The use of implicit methods for ODEs, e.g. implicit Runge-Kutta schemes, requires the solution of nonlinear systems of algebraic equations of dimension s โ€ข m, where m is the size of the continuous differential problem to be approximated. Usually, the solution of this system represents the most time-consuming section in the implementation of such methods. Consequently, the efficient solution of this section would improve their performance. In this paper, we propose a new iterative procedure to solve such equations on sequential computers.

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