Confederated modular differential equation APIs for accelerated algorithm development and benchmarking
•A Julia-based type-dispatch API is used to build a confederated system where researchers can use to add their own methods to the standard Julia differential equations ecosystem without requiring modification of core packages.•Polyalgorithms over the available methods in the ecosystem are utilized t...
Uloženo v:
| Vydáno v: | Advances in engineering software (1992) Ročník 132; s. 1 - 6 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Ltd
01.06.2019
|
| Témata: | |
| ISSN: | 0965-9978 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | •A Julia-based type-dispatch API is used to build a confederated system where researchers can use to add their own methods to the standard Julia differential equations ecosystem without requiring modification of core packages.•Polyalgorithms over the available methods in the ecosystem are utilized to give intelligent default behavior for end users.•The system allows for directly specifying the choice of algorithm in end user software, make it easy to utilize production scientific software as the benchmarking platform for the differential equation solvers.
Performant numerical solving of differential equations is required for large-scale scientific modeling. In this manuscript we focus on two questions: (1) how can researchers empirically verify theoretical advances and consistently compare methods in production software settings and (2) how can users (scientific domain experts) keep up with the state-of-the-art methods to select those which are most appropriate? Here we describe how the confederated modular API of DifferentialEquations.jl addresses these concerns. We detail the package-free API which allows numerical methods researchers to readily utilize and benchmark any compatible method directly in full-scale scientific applications. In addition, we describe how the complexity of the method choices is abstracted via a polyalgorithm. We show how scientific tooling built on top of DifferentialEquations.jl, such as packages for dynamical systems quantification and quantum optics simulation, both benefit from this structure and provide themselves as convenient benchmarking tools. |
|---|---|
| AbstractList | •A Julia-based type-dispatch API is used to build a confederated system where researchers can use to add their own methods to the standard Julia differential equations ecosystem without requiring modification of core packages.•Polyalgorithms over the available methods in the ecosystem are utilized to give intelligent default behavior for end users.•The system allows for directly specifying the choice of algorithm in end user software, make it easy to utilize production scientific software as the benchmarking platform for the differential equation solvers.
Performant numerical solving of differential equations is required for large-scale scientific modeling. In this manuscript we focus on two questions: (1) how can researchers empirically verify theoretical advances and consistently compare methods in production software settings and (2) how can users (scientific domain experts) keep up with the state-of-the-art methods to select those which are most appropriate? Here we describe how the confederated modular API of DifferentialEquations.jl addresses these concerns. We detail the package-free API which allows numerical methods researchers to readily utilize and benchmark any compatible method directly in full-scale scientific applications. In addition, we describe how the complexity of the method choices is abstracted via a polyalgorithm. We show how scientific tooling built on top of DifferentialEquations.jl, such as packages for dynamical systems quantification and quantum optics simulation, both benefit from this structure and provide themselves as convenient benchmarking tools. |
| Author | Nie, Qing Rackauckas, Christopher |
| Author_xml | – sequence: 1 givenname: Christopher orcidid: 0000-0001-5850-0663 surname: Rackauckas fullname: Rackauckas, Christopher email: accounts@chrisrackauckas.com, crackauc@mit.edu organization: Department of Mathematics, Massachusetts Institute of Technology, MA 02139, USA – sequence: 2 givenname: Qing surname: Nie fullname: Nie, Qing organization: Department of Mathematics, University of California, Irvine, CA 92697, USA |
| BookMark | eNqNkM1OAjEURrvAREDfoS8wYzudn3ZjgsQfEhJd6Lop7S0UZ1rsFBLf3kFITNzo6q7Oyf3OBI188IAQpiSnhNY321yZA_h1H2zKC0JFTlhOiBihMRF1lQnR8Es06fstIbQkBR0jOw_egoGoEhjcBbNvVcTGWQsRfHKqxfCxV8kFj2cvix7bELHSGtozotp1iC5tOmzgAG3YdQOGlTd4BV5vOhXfnV9foQur2h6uz3eK3h7uX-dP2fL5cTGfLTPNap4yrpWugdEaBKkKaqqCacaMpVxzDo1tisYUK1WXBV8Bt6KCkipRMqOgFLoCNkW3J6-Ooe8jWKld-v4-ReVaSYk8lpJb-VNKHktJwuRQahDwX4JddMOIz_-gdycUhoEHB1H22g0NwLgIOkkT3N-SLy0Kkb0 |
| CitedBy_id | crossref_primary_10_1002_adom_202400228 crossref_primary_10_1038_s41598_022_12774_5 crossref_primary_10_1093_mnras_stac1857 crossref_primary_10_3390_bioengineering11121262 crossref_primary_10_3390_asi7030035 crossref_primary_10_1016_j_enconman_2025_120080 crossref_primary_10_1016_j_jocs_2024_102287 crossref_primary_10_3390_math11081787 crossref_primary_10_1016_j_apenergy_2024_123692 crossref_primary_10_1016_j_ifacol_2023_01_004 crossref_primary_10_1038_s41535_021_00331_8 crossref_primary_10_1016_j_tca_2021_178935 crossref_primary_10_1002_kin_21753 crossref_primary_10_1371_journal_pone_0251242 crossref_primary_10_1029_2024JH000132 crossref_primary_10_1063_5_0037856 crossref_primary_10_1371_journal_pcbi_1011946 |
| Cites_doi | 10.5334/jors.151 10.1137/141000671 10.1137/0904010 10.1137/S1064827594276424 10.18637/jss.v033.i09 10.21105/joss.00598 10.1016/j.cpc.2018.02.004 10.1145/1089014.1089020 10.1016/S0377-0427(99)00134-X 10.1016/j.camwa.2011.06.002 |
| ContentType | Journal Article |
| Copyright | 2019 |
| Copyright_xml | – notice: 2019 |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.advengsoft.2019.03.009 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Engineering Computer Science |
| EndPage | 6 |
| ExternalDocumentID | 10_1016_j_advengsoft_2019_03_009 S0965997818310251 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1~. 1~5 23M 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO AAYFN ABBOA ABFNM ABJNI ABMAC ABXDB ABYKQ ACDAQ ACGFS ACNNM ACRLP ACZNC ADBBV ADEZE ADJOM ADMUD ADTZH AEBSH AECPX AEKER AENEX AFFNX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHZHX AIALX AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA GBOLZ HLZ HVGLF HZ~ IHE J1W JJJVA KOM LG9 LY7 M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SBC SDF SDG SDP SES SET SEW SPC SPCBC SST SSV SSZ T5K TN5 WUQ XPP ZMT ~G- 9DU AATTM AAXKI AAYWO AAYXX ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD |
| ID | FETCH-LOGICAL-c368t-8cac6e316e90521d523c33df18c88e7f727d2ba6428be8f95e41a943dae49c5e3 |
| ISICitedReferencesCount | 22 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000465171000001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0965-9978 |
| IngestDate | Sat Nov 29 07:02:32 EST 2025 Tue Nov 18 21:58:22 EST 2025 Fri Feb 23 02:27:54 EST 2024 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Julia Type-specialization API Design Generic programming Polyalgorithms Differential equations |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c368t-8cac6e316e90521d523c33df18c88e7f727d2ba6428be8f95e41a943dae49c5e3 |
| ORCID | 0000-0001-5850-0663 |
| OpenAccessLink | https://www.sciencedirect.com/science/article/am/pii/S0965997818310251 |
| PageCount | 6 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_advengsoft_2019_03_009 crossref_primary_10_1016_j_advengsoft_2019_03_009 elsevier_sciencedirect_doi_10_1016_j_advengsoft_2019_03_009 |
| PublicationCentury | 2000 |
| PublicationDate | June 2019 2019-06-00 |
| PublicationDateYYYYMMDD | 2019-06-01 |
| PublicationDate_xml | – month: 06 year: 2019 text: June 2019 |
| PublicationDecade | 2010 |
| PublicationTitle | Advances in engineering software (1992) |
| PublicationYear | 2019 |
| Publisher | Elsevier Ltd |
| Publisher_xml | – name: Elsevier Ltd |
| References | Soetaert, Petzoldt, Setzer (bib0021) 2010; 33 Bezanson, Edelman, Karpinski, Shah (bib0002) 2017; 59 Rackauckas (bib0016) 2018 C. Rackauckas, Q. Nie, Stability-optimized high order methods and stiffness detection for pathwise stiff stochastic differential equations, (2018). Datseris (bib0004) 2018; 3 Hairer, Wanner (bib0008) 1999; 111 Rackauckas, Nie (bib0018) 2017; 5 Hairer, Wanner (bib0007) 1991 L. Petzold, Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations, 1983, 10.1137/0904010. Veltz, Rackauckas, Frost (bib0023) 2017 Rackauckas (bib0015) 2018 Rackauckas, Arakaki (bib0017) 2018 Bezanson, Chen, Chung, Karpinski, Shah, Vitek, Zoubritzky (bib0001) 2018; 2 Pedregosa, Varoquaux, Gramfort, Michel, Thirion, Grisel, Blondel, Prettenhofer, Weiss, Dubourg, Vanderplas, Passos, Cournapeau (bib0012) 2011 Shampine, Reichelt (bib0020) 1997; 18 Hairer, Norsett, Wanner (bib0006) 2009 Jones, Oliphant, Peterson, others (bib0010) 2001 Kramer, Plankensteiner, Ostermann, Ritsch (bib0011) 2018; 227 Biernat, Rackauckas (bib0003) 2016 Hindmarsh, Brown, Grant, Lee, Serban, Shumaker, Woodward (bib0009) 2005; 31 Forst (bib0005) 2016 L. Petzold, Description of dassl: a differential/algebraic system solver (1982). Tsitouras (bib0022) 2011; 62 Rackauckas (10.1016/j.advengsoft.2019.03.009_bib0017) 2018 Bezanson (10.1016/j.advengsoft.2019.03.009_bib0002) 2017; 59 Forst (10.1016/j.advengsoft.2019.03.009_bib0005) 2016 Soetaert (10.1016/j.advengsoft.2019.03.009_bib0021) 2010; 33 Biernat (10.1016/j.advengsoft.2019.03.009_bib0003) 2016 Rackauckas (10.1016/j.advengsoft.2019.03.009_bib0016) 2018 10.1016/j.advengsoft.2019.03.009_bib0019 Kramer (10.1016/j.advengsoft.2019.03.009_bib0011) 2018; 227 Tsitouras (10.1016/j.advengsoft.2019.03.009_bib0022) 2011; 62 Hairer (10.1016/j.advengsoft.2019.03.009_sbref0006) 2009 Rackauckas (10.1016/j.advengsoft.2019.03.009_bib0018) 2017; 5 Bezanson (10.1016/j.advengsoft.2019.03.009_bib0001) 2018; 2 Shampine (10.1016/j.advengsoft.2019.03.009_bib0020) 1997; 18 Pedregosa (10.1016/j.advengsoft.2019.03.009_bib0012) 2011 Veltz (10.1016/j.advengsoft.2019.03.009_bib0023) 2017 Jones (10.1016/j.advengsoft.2019.03.009_bib0010) 2001 10.1016/j.advengsoft.2019.03.009_bib0014 Hindmarsh (10.1016/j.advengsoft.2019.03.009_bib0009) 2005; 31 Rackauckas (10.1016/j.advengsoft.2019.03.009_bib0015) 2018 Hairer (10.1016/j.advengsoft.2019.03.009_bib0007) 1991 Datseris (10.1016/j.advengsoft.2019.03.009_bib0004) 2018; 3 Hairer (10.1016/j.advengsoft.2019.03.009_bib0008) 1999; 111 10.1016/j.advengsoft.2019.03.009_bib0013 |
| References_xml | – volume: 59 start-page: 65 year: 2017 end-page: 98 ident: bib0002 article-title: Julia: a fresh approach to numerical computing publication-title: SIAM Rev – volume: 33 start-page: 1 year: 2010 end-page: 25 ident: bib0021 article-title: Solving differential equations in r: Package desolve publication-title: J Stat Softw – reference: L. Petzold, Description of dassl: a differential/algebraic system solver (1982). – reference: L. Petzold, Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations, 1983, 10.1137/0904010. – year: 2018 ident: bib0016 article-title: Diffeqr – volume: 2 year: 2018 ident: bib0001 article-title: Julia: dynamism and performance reconciled by design publication-title: PACMPL – year: 2016 ident: bib0005 article-title: Liblsoda – volume: 227 start-page: 109 year: 2018 end-page: 116 ident: bib0011 article-title: QuantumOptics.jl: a Julia framework for simulating open quantum systems publication-title: Comput Phys Commun – volume: 31 start-page: 363 year: 2005 end-page: 396 ident: bib0009 article-title: SUNDIALS: suite of nonlinear and differential/algebraic equation solvers publication-title: ACM Trans Math Softw – volume: 3 start-page: 598 year: 2018 ident: bib0004 article-title: DynamicalSystems.jl: a julia software library for chaos and nonlinear dynamics publication-title: J Open Source Software – volume: 62 start-page: 770 year: 2011 end-page: 775 ident: bib0022 article-title: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption publication-title: Comput Math Appl – volume: 111 start-page: 93 year: 1999 end-page: 111 ident: bib0008 article-title: Stiff differential equations solved by Radau methods publication-title: J Comput Appl Math – year: 2018 ident: bib0015 article-title: A comparison between differential equation solver suites in matlab, r, julia, python, c, mathematica, maple, and fortran publication-title: Winnower – start-page: 6 year: 2011 ident: bib0012 article-title: Scikit-learn: machine learning in python publication-title: Mach Learn Python – volume: 18 start-page: 1 year: 1997 end-page: 22 ident: bib0020 article-title: The matlab ode suite publication-title: SIAM J Sci Comput – year: 2016 ident: bib0003 article-title: DASSL.jl – year: 2017 ident: bib0023 article-title: LSODA.jl – year: 2009 ident: bib0006 article-title: Solving ordinary differential equations I: nonstiff problems publication-title: Springer series in computational mathematics – year: 1991 ident: bib0007 article-title: Solving ordinary differential equations II - stiff and differential-algebraic problems – year: 2018 ident: bib0017 article-title: Diffeqpy – reference: C. Rackauckas, Q. Nie, Stability-optimized high order methods and stiffness detection for pathwise stiff stochastic differential equations, (2018). – year: 2001 ident: bib0010 article-title: Scipy: open source scientific tools for Python – volume: 5 start-page: 15 year: 2017 ident: bib0018 article-title: DifferentialEquations.jl - a performant and feature-rich ecosystem for solving differential equations in julia publication-title: J Open Res Softw – ident: 10.1016/j.advengsoft.2019.03.009_bib0013 – year: 2016 ident: 10.1016/j.advengsoft.2019.03.009_bib0003 – year: 2001 ident: 10.1016/j.advengsoft.2019.03.009_bib0010 – volume: 5 start-page: 15 year: 2017 ident: 10.1016/j.advengsoft.2019.03.009_bib0018 article-title: DifferentialEquations.jl - a performant and feature-rich ecosystem for solving differential equations in julia publication-title: J Open Res Softw doi: 10.5334/jors.151 – volume: 2 issue: OOPSLA year: 2018 ident: 10.1016/j.advengsoft.2019.03.009_bib0001 article-title: Julia: dynamism and performance reconciled by design publication-title: PACMPL – volume: 59 start-page: 65 year: 2017 ident: 10.1016/j.advengsoft.2019.03.009_bib0002 article-title: Julia: a fresh approach to numerical computing publication-title: SIAM Rev doi: 10.1137/141000671 – year: 1991 ident: 10.1016/j.advengsoft.2019.03.009_bib0007 – ident: 10.1016/j.advengsoft.2019.03.009_bib0014 doi: 10.1137/0904010 – volume: 18 start-page: 1 issue: 1 year: 1997 ident: 10.1016/j.advengsoft.2019.03.009_bib0020 article-title: The matlab ode suite publication-title: SIAM J Sci Comput doi: 10.1137/S1064827594276424 – year: 2009 ident: 10.1016/j.advengsoft.2019.03.009_sbref0006 article-title: Solving ordinary differential equations I: nonstiff problems – volume: 33 start-page: 1 issue: 9 year: 2010 ident: 10.1016/j.advengsoft.2019.03.009_bib0021 article-title: Solving differential equations in r: Package desolve publication-title: J Stat Softw doi: 10.18637/jss.v033.i09 – volume: 3 start-page: 598 issue: 23 year: 2018 ident: 10.1016/j.advengsoft.2019.03.009_bib0004 article-title: DynamicalSystems.jl: a julia software library for chaos and nonlinear dynamics publication-title: J Open Source Software doi: 10.21105/joss.00598 – year: 2016 ident: 10.1016/j.advengsoft.2019.03.009_bib0005 – start-page: 6 year: 2011 ident: 10.1016/j.advengsoft.2019.03.009_bib0012 article-title: Scikit-learn: machine learning in python publication-title: Mach Learn Python – year: 2018 ident: 10.1016/j.advengsoft.2019.03.009_bib0017 – volume: 227 start-page: 109 year: 2018 ident: 10.1016/j.advengsoft.2019.03.009_bib0011 article-title: QuantumOptics.jl: a Julia framework for simulating open quantum systems publication-title: Comput Phys Commun doi: 10.1016/j.cpc.2018.02.004 – volume: 31 start-page: 363 year: 2005 ident: 10.1016/j.advengsoft.2019.03.009_bib0009 article-title: SUNDIALS: suite of nonlinear and differential/algebraic equation solvers publication-title: ACM Trans Math Softw doi: 10.1145/1089014.1089020 – year: 2018 ident: 10.1016/j.advengsoft.2019.03.009_bib0015 article-title: A comparison between differential equation solver suites in matlab, r, julia, python, c, mathematica, maple, and fortran publication-title: Winnower – year: 2018 ident: 10.1016/j.advengsoft.2019.03.009_bib0016 – volume: 111 start-page: 93 year: 1999 ident: 10.1016/j.advengsoft.2019.03.009_bib0008 article-title: Stiff differential equations solved by Radau methods publication-title: J Comput Appl Math doi: 10.1016/S0377-0427(99)00134-X – year: 2017 ident: 10.1016/j.advengsoft.2019.03.009_bib0023 – ident: 10.1016/j.advengsoft.2019.03.009_bib0019 – volume: 62 start-page: 770 issue: 2 year: 2011 ident: 10.1016/j.advengsoft.2019.03.009_bib0022 article-title: Runge–Kutta pairs of order 5(4) satisfying only the first column simplifying assumption publication-title: Comput Math Appl doi: 10.1016/j.camwa.2011.06.002 |
| SSID | ssj0014021 |
| Score | 2.3867307 |
| Snippet | •A Julia-based type-dispatch API is used to build a confederated system where researchers can use to add their own methods to the standard Julia differential... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 1 |
| SubjectTerms | API Design Differential equations Generic programming Julia Polyalgorithms Type-specialization |
| Title | Confederated modular differential equation APIs for accelerated algorithm development and benchmarking |
| URI | https://dx.doi.org/10.1016/j.advengsoft.2019.03.009 |
| Volume | 132 |
| WOSCitedRecordID | wos000465171000001&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 issn: 0965-9978 databaseCode: AIEXJ dateStart: 19950101 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0014021 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELbQlgMceBQQLQ_5wK0KWtt52OK0QkWUQ1WgSHuLHGfSB91s2U1Lfz7j2E4stBJFiMNGkaVZJ5kv4_HkmxlC3iiheQWCJ9MmK5K0YizRUEPSNFKDxiVlmjV9s4ni8FDO5-rIU4fWfTuBom3lzY26_K-qxjFUtk2d_Qt1D3-KA3iOSscjqh2Pt1J8n8Nn62laX3KxrHueaeiD0tkAOfxw9b33ZkcHa0ejNAaXHyeiL06Wq7PudBESqgYaeoW3ebrQfXQ9dmpnjkfQM2thrG-4t0YT_9Myy2wxKKV4FHX4os13fYW_3yscjN9J-kjr5zCVD0zYXKg8DkwMGTMjPakPO-ZZopRr2zNYYB_idDaURYtxvtHKu4DD-Vtd44JwYm_GcvR8tVo1rmwD3_CrndbOymxfNW5T7rd4kSk5IVuzg_35p-HDE26n-yaL4TI9-ctRAjfPt9mjibyU40fkgd9e0JmDxWNyB9pt8tBvNag35GscCt08wtg2uR-VpnxCmhhG1MOIxjCiAUbUwogijGgEIzrAiEYwoggjGsPoKfn2Yf_4_cfE9-RIjMhll0ijTQ6C5aBs2nedcWGEqBsmjZRQNOgO17zSdldbgWxUBinTKhW1hlSZDMQzMmmXLTwn1JaiVLLibAqQpniuTM3RcNQ8B1ZUYocU4bmWxhest31TLsrATDwvR42UViPlVJSokR3CBslLV7TlFjLvgupK73w6p7JE1P1RevefpF-Qe-ML9JJMutUVvCJ3zXV3tl699hD9BVrHtS0 |
| linkProvider | Elsevier |
| 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=article&rft.atitle=Confederated+modular+differential+equation+APIs+for+accelerated+algorithm+development+and+benchmarking&rft.jtitle=Advances+in+engineering+software+%281992%29&rft.au=Rackauckas%2C+Christopher&rft.au=Nie%2C+Qing&rft.date=2019-06-01&rft.pub=Elsevier+Ltd&rft.issn=0965-9978&rft.volume=132&rft.spage=1&rft.epage=6&rft_id=info:doi/10.1016%2Fj.advengsoft.2019.03.009&rft.externalDocID=S0965997818310251 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0965-9978&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0965-9978&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0965-9978&client=summon |