Title: Parallel block codes for solving large systems of ordinary differential equations

Authors: Zanariah Abdul Majid, Mohamed B. Suleiman

Addresses: Faculty of Science, Department of Mathematics, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia. ' Faculty of Science, Department of Mathematics, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia

Abstract: The two-point fully implicit block methods are developed for solving large systems of ordinary differential equations (ODEs) using variable step size on a parallel shared memory computer. The method calculates the numerical solution at two equally spaced points simultaneously within a block. The sequential and parallel performances of these methods are compared with the performances of the two-point block method using variable step size and order developed earlier by Omar (1999). For large problems, the parallel implementation produced a good speedup with respect to the sequential timing and hence better efficiency for the methods developed. The stability of the methods is also investigated.

Keywords: numerical methods; parallel method; block method; parallel block codes; large systems; ordinary differential equations; ODE; parallel computing.

DOI: 10.1504/IJSPM.2006.009018

International Journal of Simulation and Process Modelling, 2006 Vol.2 No.1/2, pp.98 - 112

Published online: 12 Feb 2006 *

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