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...
Saved in:
| Published in: | IEEE transactions on magnetics Vol. 27; no. 5; pp. 3792 - 3797 |
|---|---|
| Main Author: | |
| Format: | Journal Article Conference Proceeding |
| Language: | English |
| Published: |
New York, NY
IEEE
01.09.1991
Institute of Electrical and Electronics Engineers |
| Subjects: | |
| ISSN: | 0018-9464, 1941-0069 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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.< > |
|---|---|
| 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. |
| Author_xml | – sequence: 1 givenname: K.R. surname: Jackson fullname: Jackson, K.R. organization: Dept. of Comput. Sci., Toronto Univ., Ont., Canada |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=5278991$$DView record in Pascal Francis |
| BookMark | eNptkMtLAzEQxoMoWKsHr55yEMHD2iT7So5FfIHgRc9LNplgJJu0ya7Q_97YVhDx9DEzv3l8c4IOffCA0DklN5QSsWBZSSUYP0AzKipaENKIQzQjhPJCVE11jE5S-shhVVMyQ7DEaYqfsMHB4JWM0jlw2E8DRKukwwOM70EnbELE1tvR5tyndBPgVQy9g2FXClFbL-MGa2sMRPBbENaTHG3w6RQdGekSnO11jt7u715vH4vnl4en2-VzoUrSjIWuQaiWVZQL01ekV4IRLUwrOShg2Z6gDBjnmpJeQ0uVLKWmpmlrLpVu-nKOrnZz83HrCdLYDTYpcE56CFPqGK_bsqFlBi_3oEzZponSK5u6VbRDdtHVrOV5WcYWO0zFkFIE0yk7bi2NUVrXUdJ9f71jWbdfzx3Xfzp-Zv7HXuxYCwC_uG3xCypejbg |
| CODEN | IEMGAQ |
| CitedBy_id | crossref_primary_10_1137_24M1649800 crossref_primary_10_1016_j_amc_2005_10_042 crossref_primary_10_1007_BF02072017 crossref_primary_10_1016_j_simpat_2014_05_002 crossref_primary_10_1137_130944230 crossref_primary_10_1080_00423114_2011_582953 crossref_primary_10_1155_2022_2375102 crossref_primary_10_1002_zamm_200108115143 crossref_primary_10_1137_0732002 crossref_primary_10_1016_j_asr_2014_06_018 crossref_primary_10_1007_s11075_024_01964_z crossref_primary_10_1137_S0036142993251413 crossref_primary_10_1007_s11044_014_9422_y crossref_primary_10_1002__SICI_1096_9128_19990825_11_10_571__AID_CPE440_3_0_CO_2 crossref_primary_10_1016_S0168_9274_96_00034_7 crossref_primary_10_1016_0168_9274_95_00114_X crossref_primary_10_1016_j_apnum_2012_06_020 crossref_primary_10_1002_zamm_201300191 crossref_primary_10_1186_s12859_017_1666_0 |
| 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 |
| ContentType | Journal Article Conference Proceeding |
| Copyright | 1992 INIST-CNRS |
| Copyright_xml | – notice: 1992 INIST-CNRS |
| DBID | AAYXX CITATION IQODW 7SP 8FD L7M |
| DOI | 10.1109/20.104928 |
| DatabaseName | CrossRef Pascal-Francis Electronics & Communications Abstracts Technology Research Database Advanced Technologies Database with Aerospace |
| DatabaseTitle | CrossRef Technology Research Database Advanced Technologies Database with Aerospace Electronics & Communications Abstracts |
| DatabaseTitleList | Technology Research Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Physics Computer Science |
| EISSN | 1941-0069 |
| EndPage | 3797 |
| ExternalDocumentID | 5278991 10_1109_20_104928 104928 |
| GroupedDBID | -~X 0R~ 29I 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACGFS ACIWK ACNCT AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD F5P HZ~ H~9 IAAWW IBMZZ ICLAB IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P RIA RIE RNS TN5 TWZ VH1 VJK XXG AAYXX CITATION IQODW RIG 7SP 8FD L7M |
| ID | FETCH-LOGICAL-c306t-d5e9c724189fb40bc920d9f7a8ece2109912e288d10bde71ca3ad1f6758acd6b3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 30 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=104928&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0018-9464 |
| IngestDate | Thu Oct 02 11:14:07 EDT 2025 Mon Jul 21 09:13:20 EDT 2025 Sat Nov 29 01:52:24 EST 2025 Tue Nov 18 21:43:54 EST 2025 Tue Aug 26 16:39:15 EDT 2025 |
| IsPeerReviewed | false |
| IsScholarly | true |
| Issue | 5 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html CC BY 4.0 |
| LinkModel | DirectLink |
| MeetingName | Fourth biennial conference on electromagnetic field computation : [selected papers], Toronto, Ontario, October 22-24, 1990 |
| MergedId | FETCHMERGED-LOGICAL-c306t-d5e9c724189fb40bc920d9f7a8ece2109912e288d10bde71ca3ad1f6758acd6b3 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| PQID | 28573613 |
| PQPubID | 23500 |
| PageCount | 6 |
| ParticipantIDs | proquest_miscellaneous_28573613 crossref_citationtrail_10_1109_20_104928 ieee_primary_104928 pascalfrancis_primary_5278991 crossref_primary_10_1109_20_104928 |
| PublicationCentury | 1900 |
| PublicationDate | 1991-09-01 |
| PublicationDateYYYYMMDD | 1991-09-01 |
| PublicationDate_xml | – month: 09 year: 1991 text: 1991-09-01 day: 01 |
| PublicationDecade | 1990 |
| PublicationPlace | New York, NY |
| PublicationPlace_xml | – name: New York, NY |
| PublicationTitle | IEEE transactions on magnetics |
| PublicationTitleAbbrev | TMAG |
| PublicationYear | 1991 |
| Publisher | IEEE Institute of Electrical and Electronics Engineers |
| Publisher_xml | – name: IEEE – name: Institute of Electrical and Electronics Engineers |
| References | ref57 ref13 ref12 gear (ref16) 1987 ref59 ref58 ref11 nevanlinna (ref46) 1987; 9 ref54 ref10 van der houwen (ref22) 1989 nelken (ref42) 1989 orel (ref50) 1989 birnu (ref5) 1987; c 36 ref19 juang (ref31) 1988 gallopoulos (ref14) 1900 ref51 juang (ref29) 1988 bales (ref2) 0; 28 xuhai (ref60) 1990 jackson (ref27) 1990 ref45 ref48 ref47 nevanlinna (ref43) 1989; 29 gear (ref17) 1988 gear (ref15) 1986 ref41 burrage (ref7) 1989 ref49 lie (ref35) 1989 ref9 ref4 ref3 ref6 ref40 ref37 ref36 burrage (ref8) 1989 ref33 ref32 gear (ref18) 1987 ref39 ref38 juang (ref30) 1990 lie (ref34) 1987 simonsen (ref53) 1990 ref24 ref23 ref26 ref25 ref21 jackson (ref28) 0 aslam (ref1) 1988 yang (ref62) 1990 tam (ref56) 1989 van der houwen (ref20) 1988 schendel (ref52) 1984 ref61 nevanlinna (ref44) 1989; 29 skeel (ref55) 1989 |
| 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 |
| SSID | ssj0014510 |
| Score | 1.4978312 |
| Snippet | The parallel solution of initial value problems for ordinary differential equations has become an active area of research. Recent developments in this area are... |
| SourceID | proquest pascalfrancis crossref ieee |
| SourceType | Aggregation Database Index Database Enrichment Source Publisher |
| StartPage | 3792 |
| 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 |
| URI | https://ieeexplore.ieee.org/document/104928 https://www.proquest.com/docview/28573613 |
| Volume | 27 |
| WOSCitedRecordID | wos104928&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Xplore customDbUrl: eissn: 1941-0069 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014510 issn: 0018-9464 databaseCode: RIE dateStart: 19650101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8QwEB5UFPTg6qq4PoN48FJp-kpyFHHxIOJBwVtpkykIpavb7YL_3kzSXRS9eCvJtJRMJ5npzHwfwKUiSJeKp4FMdBJQa2UgjTW8TJjYyFAnWDmc2Qfx-ChfX9VTj7PtemEQ0RWf4TVduly-meiOfpVZC09UJFdhVYjMt2otEwZJyn23CZfEGp_0IEI8VDa8v_Y3_jh6HJcKVUIWrV2MyrNY_NqQ3SkzHvzr_XZgu3cm2Y3X_i6sYDOEwYKogfV2O4Stb6iDQ9hwVZ-63QO8YW03neMnm1SMQMDrGmvWdD6LUzNPL90y69iyN6oysmOEDo6s56HxUzZ-dV29bMG24gTxw6OIt_vwMr57vr0Pet6FQNsAYhaYFJUW9miXqiqTsNQqCo2qRCFRY0SpNB5hJKXhYWlQcF3EheEVhR6FNlkZH8BaM2nwEFgsZZHFOsMQraNTCmUKFVPMZbeZyJTpCK4WKsl1D0pO3Bh17oKTUOURJclpWUdwsRR990gcfwkNSS3fBPzo6Q81L6dT6gNWfATnC7Xn1rooZVI0OOnaPJKpiK3Hc_Tnc49h01eOUcnZCazNph2ewrqez97a6Zn7QL8ALfnlsg |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1NT9wwEB0VCqI9lLJQdcuXhThwCYodZ2MfEWJFxbLiQCVuUWJPJKQo2242SP339djZFaty4RbZkyjyZOyZzMx7AOeaIF0qnkZKGhlRa2WkrDO8UWYTq2IjsfI4s5NsOlVPT_qhx9n2vTCI6IvP8JIufS7fzkxHv8qchUst1AZ8TKUUcWjWWqUMZMpDvwlXxBsvexghHmsX4F-GW9cOH8-mQrWQReuWowo8Fv9tyf6cGe--6w2_wpfenWRXQf978AGbAewuqRpYb7kD-PwKd3AA277u07T7gFes7eYv-JfNKkYw4HWNNWu6kMepWSCYbplzbdkz1Rm5McIHR9Yz0YQpF8H6vl625Fvxgvgn4Ii3B_BrfPN4fRv1zAuRcSHEIrIpapO5w13pqpRxabSIra6yQqFBQck0LlAoZXlcWsy4KZLC8oqCj8LYUZl8g81m1uB3YIlSxSgxI4zRuTplpm2hE4q63EYjbJkO4WKpktz0sOTEjlHnPjyJdS4oTU7LOoSzlejvgMXxltCA1PJKIIwer6l5NZ1SJ7DmQzhdqj139kVJk6LBWdfmQqVZ4nyeH28-9xR2bh_vJ_nk5_TuED6FOjIqQDuCzcW8w2PYMi-L53Z-4j_Wfz8g6Pk |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=proceeding&rft.title=IEEE+transactions+on+magnetics&rft.atitle=A+survey+of+parallel+numerical+methods+for+initial+value+problems+for+ordinary+differential+equations&rft.au=JACKSON%2C+K.+R&rft.date=1991-09-01&rft.pub=Institute+of+Electrical+and+Electronics+Engineers&rft.issn=0018-9464&rft.volume=27&rft.issue=5&rft.spage=3792&rft.epage=3797&rft_id=info:doi/10.1109%2F20.104928&rft.externalDBID=n%2Fa&rft.externalDocID=5278991 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9464&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9464&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9464&client=summon |