Parallel iteration of high-order Runge-Kutta methods with stepsize control
Journal of Computational and Applied Mathematics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Hypercube Implementation and Performance Analysis for Extrapolation Models
CONPAR 94 - VAPP VI Proceedings of the Third Joint International Conference on Vector and Parallel Processing: Parallel Processing
Iterated Runge-Kutta methods on distributed memory multiprocessors
PDP '95 Proceedings of the 3rd Euromicro Workshop on Parallel and Distributed Processing
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The spatial discretization of nonlinear partial differential equations (PDEs) results in large systems of nonlinear ordinary differential equations (ODEs). The discretization of the Brusselator equation is a characteristic example. For the parallel numerical solution of the Brusselator equation we use an iterated Runge-Kutta method. We propose modifications of the original method that exploit the access structure of the Brusselator equation. The implementation is realized on an Intel iPSC/860. A theoretical analysis of the resulting speedup values shows that the efficiency cannot be improved considerably.