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http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/145
Title: | On the use of parallel processors for implicit Runge-Kutta methods |
Authors: | Cooper, G.J Vignesvaran, R |
Keywords: | AMS Subject Classification: AMS (MOS) 65L05;Implementation;implicit methods;parallel processing;Runge-Kutta |
Issue Date: | Jun-1993 |
Publisher: | Springer-Verlag |
Abstract: | An iteration scheme, for solving the non-linear equations arising in the implementation of implicit Runge-Kutta methods, is proposed. This scheme is particularly suitable for parallel computation and can be applied to any method which has a coefficient matrix A with all eigenvalues real (and positive). For such methods, the efficiency of a modified Newton scheme may often be improved by the use of a similarity transformation of A but, even when this is the case, the proposed scheme can have advantages for parallel computation. Numerical results illustrate this. The new scheme converges in a finite number of iterations when applied to linear systems of differential equations, achieving this by using the nilpotency of a strictly lower triangular matrix S-1AS - Λ, with Λ a diagonal matrix. The scheme reduces to the modified Newton scheme when S-1AS is diagonal. A convergence result is obtained which is applicable to nonlinear stiff systems. |
URI: | http://repo.lib.jfn.ac.lk/ujrr/handle/123456789/145 |
ISSN: | 0010485X |
Appears in Collections: | Mathematics and Statistics |
Files in This Item:
File | Description | Size | Format | |
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On the use of parallel processors for implicit Runge-Vignesvaran.pdf | 178.09 kB | Adobe PDF | View/Open |
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