A survey of parallel numerical methods for initial value problems for ordinary differential equations
The parallel solution of initial value problems for ordinary differential equations has become an active area of research. Recent developments in this area are surveyed with particular emphasis on traditional forward-step methods that offer the potential for effective small-scale parallelism on exis...
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| Vydáno v: | IEEE transactions on magnetics Ročník 27; číslo 5; s. 3792 - 3797 |
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| Hlavní autor: | |
| Médium: | Journal Article Konferenční příspěvek |
| Jazyk: | angličtina |
| Vydáno: |
New York, NY
IEEE
01.09.1991
Institute of Electrical and Electronics Engineers |
| Témata: | |
| ISSN: | 0018-9464, 1941-0069 |
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| Abstract | The parallel solution of initial value problems for ordinary differential equations has become an active area of research. Recent developments in this area are surveyed with particular emphasis on traditional forward-step methods that offer the potential for effective small-scale parallelism on existing machines.< > |
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| AbstractList | The parallel solution of initial value problems for ordinary differential equations has become an active area of research. Recent developments in this area are surveyed with particular emphasis on traditional forward-step methods that offer the potential for effective small-scale parallelism on existing machines.< > |
| Author | Jackson, K.R. |
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| Cites_doi | 10.1109/TC.1976.1674545 10.1016/0898-1221(77)90097-9 10.1137/0908039 10.1145/355588.365137 10.1109/TCAD.1984.1270089 10.1007/BFb0089233 10.1007/BF01934186 10.1007/BF01932265 10.1109/TC.1978.1675121 10.1145/63047.63129 10.1109/TC.1987.1676902 10.1007/BFb0089229 10.1137/0910046 10.1007/BF02219239 10.2172/5005850 10.1016/0377-0427(90)90200-J 10.1016/0377-0427(89)90026-5 10.1145/318789.318793 10.1137/0913061 10.1109/DAC.1990.114890 10.1016/0168-9274(85)90007-8 10.1007/BF01932708 10.1145/42411.42415 10.1080/01630568708816241 10.1109/TCAD.1982.1270004 10.1137/1013094 10.2172/6913318 10.1007/BF01937277 10.1137/0908046 10.1137/0908012 10.1016/0377-0427(90)90170-5 10.2307/2003233 10.1007/BF01994887 10.1007/BF01952687 10.1007/BFb0089234 10.1137/0909074 10.1093/imanum/10.4.463 |
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| References_xml | – ident: ref59 doi: 10.1109/TC.1976.1674545 – ident: ref32 doi: 10.1016/0898-1221(77)90097-9 – year: 1988 ident: ref1 publication-title: Asynchronous integration of ordinary differential equations on multiprocessors – year: 1989 ident: ref50 publication-title: Real pole approximations to the exponential function – year: 1986 ident: ref15 publication-title: The Potential for Parallelism in Ordinary Differential Equations – ident: ref11 doi: 10.1137/0908039 – ident: ref48 doi: 10.1145/355588.365137 – year: 1987 ident: ref18 publication-title: Explicit stiff stability via splitting and the parallel solution of ODEs – ident: ref47 doi: 10.1109/TCAD.1984.1270089 – year: 1984 ident: ref52 publication-title: Introduction to Numerical Methods for Parallel Computers – year: 1987 ident: ref16 publication-title: The parallel pnethods for ordinary differential equations – ident: ref45 doi: 10.1007/BFb0089233 – ident: ref36 doi: 10.1007/BF01934186 – ident: ref9 doi: 10.1007/BF01932265 – ident: ref12 doi: 10.1109/TC.1978.1675121 – ident: ref6 doi: 10.1145/63047.63129 – volume: c 36 start-page: 299 year: 1987 ident: ref5 article-title: Parallel block predictor-corrector methods for ode's publication-title: IEEE Trans Comp doi: 10.1109/TC.1987.1676902 – ident: ref3 doi: 10.1007/BFb0089229 – ident: ref54 doi: 10.1137/0910046 – volume: 29 start-page: 535 year: 1989 ident: ref44 article-title: Remarks on Picard-Lindelof iteration: Part II publication-title: BIT doi: 10.1007/BF02219239 – year: 1990 ident: ref30 publication-title: Waveform methods for ordinary differential equations doi: 10.2172/5005850 – ident: ref21 doi: 10.1016/0377-0427(90)90200-J – ident: ref23 doi: 10.1016/0377-0427(89)90026-5 – ident: ref13 doi: 10.1145/318789.318793 – year: 1990 ident: ref62 publication-title: PARASPICE A Parallel Direct Circuit Simulator for Shared-Memory Multiprocessors – ident: ref58 doi: 10.1137/0913061 – year: 1989 ident: ref22 publication-title: Embedded diagonally implicit Runge-Kutta algorithms on parallel computers – ident: ref61 doi: 10.1109/DAC.1990.114890 – year: 1989 ident: ref56 publication-title: Parallel methods for the numerical solution of ordinary differential equations – year: 1988 ident: ref31 publication-title: Accuracy increase in waveform Gauss Seidel – ident: ref57 doi: 10.1137/0913061 – year: 0 ident: ref28 article-title: The potential for parallelism in Runge-Kutta methods. Part 2: RK predictor-corrector formulas publication-title: Math Comp – year: 1989 ident: ref42 article-title: Parallel methods in sensitivity analysis publication-title: Proc Fourth Conf Hypercubes – ident: ref10 doi: 10.1016/0168-9274(85)90007-8 – ident: ref25 doi: 10.1007/BF01932708 – ident: ref19 doi: 10.1145/42411.42415 – volume: 9 start-page: 435 year: 1987 ident: ref46 article-title: Remarks on the convergence of waveform relaxation method publication-title: Numer Fund Anal and Optimiz doi: 10.1080/01630568708816241 – year: 1989 ident: ref35 publication-title: Relaxation-based integration by Rurige-Kutta methods and its application to moving finite element methods – year: 1987 ident: ref34 publication-title: Some aspects of parallel Runge-Kutta methods – year: 1989 ident: ref8 publication-title: The error behaviour of a general class of predictor-corrector methods – ident: ref33 doi: 10.1109/TCAD.1982.1270004 – ident: ref40 doi: 10.1137/1013094 – year: 1990 ident: ref60 publication-title: Potential performance of methods for parallelism across time in ODEs doi: 10.2172/6913318 – volume: 28 start-page: 70 year: 0 ident: ref2 article-title: On the A0 acceptability of rational approximations to the exponential function with only real poles publication-title: BIT – ident: ref38 doi: 10.1007/BF01937277 – ident: ref37 doi: 10.1137/0908046 – year: 1900 ident: ref14 publication-title: Efficient solution of parabolic equations by polynomial approximation methods – year: 1988 ident: ref20 publication-title: Variable step iteration of high-order Runge-Kutta methods on parallel computers – year: 1990 ident: ref53 publication-title: Extrapolation methods for ODE's continuous approximations a parallel approach – year: 1988 ident: ref17 publication-title: Massive parallelism across the method in ODEs – year: 1988 ident: ref29 publication-title: Accuracy increase in waveform relaxation – ident: ref41 doi: 10.1137/0908012 – ident: ref4 doi: 10.1016/0377-0427(90)90170-5 – ident: ref39 doi: 10.2307/2003233 – ident: ref51 doi: 10.1007/BF01994887 – volume: 29 start-page: 328 year: 1989 ident: ref43 article-title: Remarks on Picard-Lindelof iteration: Part I publication-title: BIT doi: 10.1007/BF01952687 – year: 1990 ident: ref27 publication-title: The potential for parallelism in Runge-Kutta methods Part 1 RK formulas in standard form – ident: ref49 doi: 10.1007/BFb0089234 – year: 1989 ident: ref55 publication-title: Potential for parallelism in explicit linear methods – ident: ref24 doi: 10.1137/0909074 – ident: ref26 doi: 10.1093/imanum/10.4.463 – year: 1989 ident: ref7 publication-title: Solving nonstiff IVPs in a transputer environment |
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| SubjectTerms | Computer architecture Computer science Concurrent computing Differential equations Electromagnetism; electron and ion optics Exact sciences and technology Fundamental areas of phenomenology (including applications) Gears Large-scale systems Linear algebra Parallel algorithms Parallel processing Physics Software testing |
| Title | A survey of parallel numerical methods for initial value problems for ordinary differential equations |
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