Clustered Diagonally Explicit Runge-Kutta Method for the Solution of Systems of Differential Equations
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چکیده
In this paper, we develop, analyze, and evaluate a parallel algorithm for diagonally explicit Runge Kutta method of order four (DERK4) for solving systems of differential equations. A timing model has been developed and verified to estimate the execution time of the proposed algorithm. We used the proposed algorithm to solve a predatorprey system and Lorenz equation numerically. The numerical results indicate that the proposed algorithm offers a reduction of both the computation time and storage requirements without losing the desired accuracy. Moreover, the obtained timing results show that the proposed algorithm provides excellent speedup and efficiency for small number of processors. KeywordsParallel Computing; Systems of Differential Equations; Runge-Kutta Methods; Predator-Prey System; Lorenz Equation
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تاریخ انتشار 2014