Parallel iteration of high-order Runge-Kutta methods with stepsize control
Journal of Computational and Applied Mathematics
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Parallel methods for initial value problems
Applied Numerical Mathematics - Special issue: parallel methods for ordinary differential equations
Massive parallelism across space in ODEs
Applied Numerical Mathematics - Special issue: parallel methods for ordinary differential equations
Parallelism across time in ODEs
Applied Numerical Mathematics - Special issue: parallel methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
Parallel and sequential methods for ordinary differential equations
A Survey of Speculative Methods for Transient State Analysis
PARELEC '02 Proceedings of the International Conference on Parallel Computing in Electrical Engineering
Iterated Runge-Kutta methods on distributed memory multiprocessors
PDP '95 Proceedings of the 3rd Euromicro Workshop on Parallel and Distributed Processing
The Modified Speculative Method for the Transient States Analysis
PARELEC '04 Proceedings of the international conference on Parallel Computing in Electrical Engineering
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In this paper a speculative method for parallel modeling of transient states analysis of electrical circuits in distributed systems is presented. Solving systems of linear or nonlinear ordinary differential equations that describe the transient states is a purely sequential process. The proposed speculative computation method converts involved sequential computations into intensively parallel ones. The general idea of this method is based on decomposition of the analysed time domain into sub-intervals in which parallel solving is done based on speculatively assumed initial conditions. Parallel computations in subsequent time sub-intervals are conducted with the use of sequential numerical Runge-Kutta method. Application of the method for simulation of functioning of a DC motor with a controlled integration step size is shown.