| Discretized Multisplitting AOR Waveform Relaxation Algorithms for Initial Value Problem of Systems of ODEs |
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| 作者姓名： | 谷同祥 李文强 |
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| 作者单位： | Department of Mathematics，Henan Normal University，Xinxiang，453002 |
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| 摘 要： | 1.IntroductionInthedevelopmentofnewelectricalcircuits,thesimulationofthebehaviourofthecircuithasbecomeanessentialtoolforelectricalengineers.Fromthelayoutofthecircuitanonlinearsystemofordinarydifferentialequationsisgeneratedwhichdescribesthedynamicalbehaviourofthecircuit.Inthesimulationofverylargescaleintegrated(VLSI)circuitsthedimensionofthesystemofODEscanbecomeverylarge.Moreoversincethesystemisstiff,solvingthesesystemsisaverycomputionallyintensivetaskandtheuseofsupercomputersbecomesin-evit…
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Discretized Multisplitting AOR Waveform Relaxation Algorithms for Initial Value Problem of Systems of ODEs |
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| Gu Tongxiang,Li Wenqiang.Discretized Multisplitting AOR Waveform Relaxation Algorithms for Initial Value Problem of Systems of ODEs[J].Chinese Quarterly Journal of Mathematics,1997(4). |
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| Authors: | Gu Tongxiang Li Wenqiang |
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| Abstract: | The multisplitting algorithm for solving large systems of ordinary differential equations on parallel computers was introduced by Jeltsch and Pohl in 1]. On fixed time intervals conver gence results could be derived if the subsystems are solving exactly.Firstly,in theis paper,we deal with an extension of the waveform relaxation algorithm by us ing multisplittin AOR method based on an overlapping block decomposition. We restricted our selves to equidistant timepoints and dealed with the case that an implicit integration method was used to solve the subsystems numerically in parallel. Then we have proved convergence of multi splitting AOR waveform relaxation algorithm on a fixed window containing a finite number of timepoints. |
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| Keywords: | systems of ordinary differential equations initial value problems multisplitting algorithm AOR method waveform relaxation algorithm |
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