✦ LIBER ✦

On Accelerating the Convergence of Nonlinear Iterative Algorithms

✍ Scribed by D.W. Black; A.P. Rothmayer

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 505 KB
Volume: 111
Category: Article
ISSN: 0021-9991
DOI: 10.1006/jcph.1994.1066

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✦ Synopsis

The underlying theory of vector sequence extrapolation methods for linear and nonlinear problems is examined. It is shown that nonlinearity limits savings in total number of iterations to (50 %) for strongly nonlinear problems when linear-based extrapolation methods are used. In support of this conclusion, convergence behaviors of solutions of Burgers' equation and an interacting boundary layer problem are examined. Supporting evidence from the work of previous researchers is also presemted. A possible means of circumventing this limitation by including nonlinear terms in the extrapolation is suggested. Results of this method for a scalar model problem and a solution to Burgers' equation are given, showing that the (50 %) limitation can be circumvented. c. 1994 Academic Press. Inc.

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