Semi-Explicit Composition Methods in Memcapacitor Circuit Simulation
Composition algorithms make up a prospective class of methods for solving ordinary differential equations. Their main advantage is an ability to retain some properties of the simulated continuous systems, e.g. phase space volume. Meanwhile, computational costs of composition solvers for non-Hamilton...
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| Published in | International journal of embedded and real-time communication systems Vol. 10; no. 2; pp. 37 - 52 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Hershey
IGI Global
01.04.2019
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1947-3176 1947-3184 |
| DOI | 10.4018/IJERTCS.2019040103 |
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| Abstract | Composition algorithms make up a prospective class of methods for solving ordinary differential equations. Their main advantage is an ability to retain some properties of the simulated continuous systems, e.g. phase space volume. Meanwhile, computational costs of composition solvers for non-Hamiltonian systems are high because the implicit midpoint rule should be used as a basic method. This also complicates the development of embedded applications based on the numerical solution of ODEs, such as hardware chaos generators. In this article, a new semi-explicit composition methods are proposed. The stability regions for different composition algorithms were plotted and a memcapacitor circuit was studied as a test problem. Computational experiments reveal the superior properties of semi-explicit composition algorithms as a hardware-targeted ODE solvers. The obtained results imply that the development of semi-explicit composition algorithms is a step towards construction a new generation of simulation software for nonlinear dynamical systems and embedded chaos generators. |
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| AbstractList | Composition algorithms make up a prospective class of methods for solving ordinary differential equations. Their main advantage is an ability to retain some properties of the simulated continuous systems, e.g. phase space volume. Meanwhile, computational costs of composition solvers for non-Hamiltonian systems are high because the implicit midpoint rule should be used as a basic method. This also complicates the development of embedded applications based on the numerical solution of ODEs, such as hardware chaos generators. In this article, a new semi-explicit composition methods are proposed. The stability regions for different composition algorithms were plotted and a memcapacitor circuit was studied as a test problem. Computational experiments reveal the superior properties of semi-explicit composition algorithms as a hardware-targeted ODE solvers. The obtained results imply that the development of semi-explicit composition algorithms is a step towards construction a new generation of simulation software for nonlinear dynamical systems and embedded chaos generators. |
| Author | Ostrovskii, Valerii Y Karimov, Artur I Andreev, Valery S Butusov, Denis N |
| AuthorAffiliation | Saint-Petersburg Electrotechnical University “LETI”, Saint Petersburg, Russia |
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| Cites_doi | 10.1016/j.cam.2005.03.011 10.1016/0375-9601(90)90962-N 10.1109/EIConRus.2017.7910542 10.1016/j.chaos.2011.12.006 10.1109/SCM.2016.7519698 10.1137/0916010 10.1016/j.future.2016.02.020 10.1109/PROC.1976.10092 10.1103/PhysRevE.72.016220 10.1109/TCT.1971.1083337 10.1007/BF02165234 10.1109/ICCCN.2011.6006010 10.1007/978-1-4899-3093-4 10.1103/PhysRevApplied.6.064028 10.1109/EIConRus.2017.7910545 10.1016/j.amc.2018.02.020 10.1080/00018732.2010.544961 10.1007/978-3-319-30279-9 10.1007/s11071-016-2990-z 10.1016/0375-9601(90)90092-3 10.1016/0375-9601(91)90404-V 10.1090/S0025-5718-97-00873-9 10.1109/JPROC.2009.2021077 |
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| References_xml | – ident: IJERTCS.2019040103-26 doi: 10.1016/j.cam.2005.03.011 – year: 1993 ident: IJERTCS.2019040103-13 publication-title: Solving Ordinary Differential Equations I. Berlin, State – ident: IJERTCS.2019040103-27 doi: 10.1016/0375-9601(90)90962-N – volume: 45 start-page: 89 year: 2008 ident: IJERTCS.2019040103-1 article-title: Splitting and composition methods in the numerical integration of differential equation. publication-title: Bol. Soc. Esp. Mat. Apl. – ident: IJERTCS.2019040103-0 doi: 10.1109/EIConRus.2017.7910542 – start-page: 162 year: 2016 ident: IJERTCS.2019040103-4 article-title: Symmetric extrapolation solvers for ordinary differential equations. publication-title: Proceedings of IEEE NW Russia Young Researchers in Electrical and Electronic Engineering Conference (ElConRusNW) – ident: IJERTCS.2019040103-23 doi: 10.1016/j.chaos.2011.12.006 – ident: IJERTCS.2019040103-3 doi: 10.1109/SCM.2016.7519698 – ident: IJERTCS.2019040103-17 doi: 10.1137/0916010 – ident: IJERTCS.2019040103-18 doi: 10.1016/j.future.2016.02.020 – ident: IJERTCS.2019040103-6 doi: 10.1109/PROC.1976.10092 – volume: 72 start-page: 16220 issue: 1 year: 2005 ident: IJERTCS.2019040103-10 article-title: Properties making a chaotic system a good pseudo random number generator. publication-title: Physical Review. E doi: 10.1103/PhysRevE.72.016220 – ident: IJERTCS.2019040103-16 – ident: IJERTCS.2019040103-12 – ident: IJERTCS.2019040103-7 doi: 10.1109/TCT.1971.1083337 – ident: IJERTCS.2019040103-2 doi: 10.1007/BF02165234 – ident: IJERTCS.2019040103-15 doi: 10.1109/ICCCN.2011.6006010 – ident: IJERTCS.2019040103-24 doi: 10.1007/978-1-4899-3093-4 – ident: IJERTCS.2019040103-25 doi: 10.1103/PhysRevApplied.6.064028 – ident: IJERTCS.2019040103-5 doi: 10.1109/EIConRus.2017.7910545 – ident: IJERTCS.2019040103-20 doi: 10.1016/j.amc.2018.02.020 – ident: IJERTCS.2019040103-22 doi: 10.1080/00018732.2010.544961 – ident: IJERTCS.2019040103-28 doi: 10.1007/978-3-319-30279-9 – start-page: 384 year: 1965 ident: IJERTCS.2019040103-11 article-title: Repeated extrapolation to the limit in the numerical solution of ordinary differential equations. publication-title: SIAM Journal on Numerical Analysis – ident: IJERTCS.2019040103-19 doi: 10.1007/s11071-016-2990-z – volume: 52 start-page: 551 issue: 2 year: 2013 ident: IJERTCS.2019040103-21 article-title: A chaotic encryption scheme for real-time embedded systems: Design and implementation. publication-title: Telecommunication Systems – ident: IJERTCS.2019040103-29 doi: 10.1016/0375-9601(90)90092-3 – ident: IJERTCS.2019040103-8 doi: 10.1016/0375-9601(91)90404-V – ident: IJERTCS.2019040103-14 doi: 10.1090/S0025-5718-97-00873-9 – ident: IJERTCS.2019040103-9 doi: 10.1109/JPROC.2009.2021077 |
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| SubjectTerms | Algorithms Circuits Communication Composition Computer simulation Computing costs Data encryption Differential equations Dynamical systems Embedded systems Hamiltonian functions Hardware Investigations Methods Nonlinear systems Numerical analysis Ordinary differential equations Simulation Software Solvers |
| Title | Semi-Explicit Composition Methods in Memcapacitor Circuit Simulation |
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