NDLI: One-Stage Parallel Methods for the Numerical Solution of Ordinary Differential Equations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Tam, H. W.
Copyright Year	1992
Abstract	This paper studies one-stage block methods for solving the numerical solution of ordinary differential equations (ODES) in parallel, and a new family of one-stage methods is introduced. Each member in this family has a stability region equal to the interior of that of the Euler method, together with the origin. Thus the stability regions remain unchanged as the order is increased. These methods lead to the discovery of a specific approach in deriving parallel ODE methods with good stability regions; zero-stable block methods with perfect power stability polynomials are considered. It is also found that the coupling between the equations of individual time points for block methods must be taken into account. The coupling between time points restricts the use of the new one-stage parallel methods. By a modification of the method parameters, this coupling effect is eliminated. The resulting one-stage parallel methods outperform the Adams-Bashforth methods in both stability and accuracy.
Starting Page	1039
Ending Page	1061
Page Count	23
File Format	PDF
ISSN	01965204
DOI	10.1137/0913061
Issue Number	5
Volume Number	13
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	one-stage block methods Initial value problems ordinary differential equations (ODEs) parallel processing
Content Type	Text
Resource Type	Article

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