Parallel Algorithms Of Simulation - Dmitrieva, Olga;Firsova, Alisa
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The paper concerns itself with the parallel algorithms based on collocation block methods and allows solving the Cauchy problem for systems of ordinary differential equations at points forming a block simultaneously. For all the developed methods the conditions for stability and order of accuracy are determined, the convergence is proven. The structure of the developed methods allows constructing algorithms for automatic integration step control, which is especially important in the simulation of objects described by stiff or ill-conditioned systems of equations. For simulation of linear…mehr

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Produktbeschreibung
The paper concerns itself with the parallel algorithms based on collocation block methods and allows solving the Cauchy problem for systems of ordinary differential equations at points forming a block simultaneously. For all the developed methods the conditions for stability and order of accuracy are determined, the convergence is proven. The structure of the developed methods allows constructing algorithms for automatic integration step control, which is especially important in the simulation of objects described by stiff or ill-conditioned systems of equations. For simulation of linear dynamic objects the approaches are proposed which allows restructuring phasic nested methods and passing from the sequential implementation to the parallel performance of computation with the control of error on a step. Engaging parallel computing systems in the process of modeling has significantly increased the dimension of the tasks and the capacity of solving of problems with special properties that arise directly in the process of mathematical modeling of behavior of dynamic objects, and in the generation of secondary systems after discretization of partial differential equations.
Autorenporträt
Alisa Firsova: graduated from Economic Cybernetics at Donetsk National Technical University, Ukraine. A student of Kyiv School of Economics, Ukraine. Olga Dmitrieva: Candidate of Science, assistant professor of Applied Mathematics and Information Science department of Donetsk National Technical University, candidate for a doctor¿s degree.