Partial differential equation (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Partial differential equation" in English language version.

Last modified: 08:46:40, 28 September 2026 (UTC)

Ref.Un. Ref.Website

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44doi.org

2^nd place

33math24.wordpress.com

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33adsabs.harvard.edu

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31stanford.edu

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22books.google.com

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22nih.gov

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11europa.eu

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11cambridge.org

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11archive.org

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11osti.gov

2,098^th place

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11arxiv.org

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adsabs.harvard.edu (Global: 14^th place; English: 9^th place)

ui.adsabs.harvard.edu

Raissi, M.; Perdikaris, P.; Karniadakis, G.E. (February 2019). "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations". Journal of Computational Physics. 378: 686–707. Bibcode:2019JCoPh.378..686R. doi:10.1016/j.jcp.2018.10.045. OSTI 1595805.
Mao, Zhiping; Jagtap, Ameya D.; Karniadakis, George Em (March 2020). "Physics-informed neural networks for high-speed flows". Computer Methods in Applied Mechanics and Engineering. 360 112789. Bibcode:2020CMAME.36012789M. doi:10.1016/j.cma.2019.112789.
Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em (28 February 2020). "Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations". Science. 367 (6481): 1026–1030. Bibcode:2020Sci...367.1026R. doi:10.1126/science.aaw4741. PMC 7219083. PMID 32001523.

archive.org (Global: 6^th place; English: 6^th place)

Gershenfeld, Neil (2000). The nature of mathematical modeling (Reprinted (with corr.) ed.). Cambridge: Cambridge University Press. p. 27. ISBN 0521570956.

arxiv.org (Global: 49^th place; English: 31^st place)

Huang, Yunfei; Greenberg, David S. (2025). "Geometric and Physical Constraints Synergistically Enhance Neural PDE Surrogates". arXiv:2506.05513 [cs.LG].

books.google.com (Global: 3^rd place; English: 3^rd place)

Wilmott, Paul; Howison, Sam; Dewynne, Jeff (1995). The Mathematics of Financial Derivatives. Cambridge University Press. pp. 76–81. ISBN 0-521-49789-2.
Adomian, G. (1994). Solving Frontier problems of Physics: The decomposition method. Kluwer Academic Publishers. ISBN 9789401582896.

cambridge.org (Global: 209^th place; English: 151^st place)

Erdoğan, M. Burak; Tzirakis, Nikolaos (2016). Dispersive Partial Differential Equations: Wellposedness and Applications. London Mathematical Society Student Texts. Cambridge: Cambridge University Press. ISBN 978-1-107-14904-5.

doi.org (Global: 2^nd place; English: 2^nd place)

Klainerman, Sergiu (2010). "PDE as a Unified Subject". In Alon, N.; Bourgain, J.; Connes, A.; Gromov, M.; Milman, V. (eds.). Visions in Mathematics. Modern Birkhäuser Classics. Basel: Birkhäuser. pp. 279–315. doi:10.1007/978-3-0346-0422-2_10. ISBN 978-3-0346-0421-5.
Raissi, M.; Perdikaris, P.; Karniadakis, G.E. (February 2019). "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations". Journal of Computational Physics. 378: 686–707. Bibcode:2019JCoPh.378..686R. doi:10.1016/j.jcp.2018.10.045. OSTI 1595805.
Mao, Zhiping; Jagtap, Ameya D.; Karniadakis, George Em (March 2020). "Physics-informed neural networks for high-speed flows". Computer Methods in Applied Mechanics and Engineering. 360 112789. Bibcode:2020CMAME.36012789M. doi:10.1016/j.cma.2019.112789.
Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em (28 February 2020). "Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations". Science. 367 (6481): 1026–1030. Bibcode:2020Sci...367.1026R. doi:10.1126/science.aaw4741. PMC 7219083. PMID 32001523.

europa.eu (Global: 62^nd place; English: 100^th place)

cordis.europa.eu

"Regularity and singularities in elliptic PDE's: beyond monotonicity formulas | EllipticPDE Project | Fact Sheet | H2020". CORDIS | European Commission. Retrieved 2024-02-05.

math24.wordpress.com (Global: low place; English: low place)

Evans 1998, pp. 1–2. Evans, Lawrence C. (1998). Partial differential equations (PDF). Providence (R. I.): American mathematical society. ISBN 0-8218-0772-2.
Evans 1998, Appendix A. Evans, Lawrence C. (1998). Partial differential equations (PDF). Providence (R. I.): American mathematical society. ISBN 0-8218-0772-2.
Evans 1998, chpt. 6. Second-Order Elliptic Equations. Evans, Lawrence C. (1998). Partial differential equations (PDF). Providence (R. I.): American mathematical society. ISBN 0-8218-0772-2.

nih.gov (Global: 5^th place; English: 5^th place)

ncbi.nlm.nih.gov

Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em (28 February 2020). "Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations". Science. 367 (6481): 1026–1030. Bibcode:2020Sci...367.1026R. doi:10.1126/science.aaw4741. PMC 7219083. PMID 32001523.

pubmed.ncbi.nlm.nih.gov

Raissi, Maziar; Yazdani, Alireza; Karniadakis, George Em (28 February 2020). "Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations". Science. 367 (6481): 1026–1030. Bibcode:2020Sci...367.1026R. doi:10.1126/science.aaw4741. PMC 7219083. PMID 32001523.

osti.gov (Global: 2,098^th place; English: 1,146^th place)

Raissi, M.; Perdikaris, P.; Karniadakis, G.E. (February 2019). "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations". Journal of Computational Physics. 378: 686–707. Bibcode:2019JCoPh.378..686R. doi:10.1016/j.jcp.2018.10.045. OSTI 1595805.

stanford.edu (Global: 194^th place; English: 182^nd place)

web.stanford.edu

Levandosky, Julie. "Classification of Second-Order Equations" (PDF).

Partial differential equation (English Wikipedia)

adsabs.harvard.edu (Global: 14th place; English: 9th place)

ui.adsabs.harvard.edu

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 49th place; English: 31st place)

books.google.com (Global: 3rd place; English: 3rd place)

cambridge.org (Global: 209th place; English: 151st place)

doi.org (Global: 2nd place; English: 2nd place)

europa.eu (Global: 62nd place; English: 100th place)