{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T09:45:12Z","timestamp":1775727912417,"version":"3.50.1"},"reference-count":10,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2014,10,30]],"date-time":"2014-10-30T00:00:00Z","timestamp":1414627200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2015,5]]},"DOI":"10.1007\/s00521-014-1762-2","type":"journal-article","created":{"date-parts":[[2014,10,29]],"date-time":"2014-10-29T06:58:14Z","timestamp":1414565894000},"page":"765-773","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":69,"title":["Artificial neural network method for solving the Navier\u2013Stokes equations"],"prefix":"10.1007","volume":"26","author":[{"given":"M.","family":"Baymani","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Effati","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Niazmand","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Kerayechian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2014,10,30]]},"reference":[{"key":"1762_CR1","first-page":"38","volume":"1","author":"V Christiano","year":"2008","unstructured":"Christiano V, Smarandache F (2008) An exact mapping from Navier\u2013Stokes equation to Schrodinger equation via Riccati equation. Prog Phys 1:38\u201339","journal-title":"Prog Phys"},{"key":"1762_CR2","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1016\/j.amc.2008.10.058","volume":"207","author":"S Dongyang","year":"2009","unstructured":"Dongyang S, Jincheng R et al (2009) A new second order nonconforming mixed finite element scheme for the stationary Stokes and Navier\u2013Stokes equations. Appl Math Comput 207:462\u2013477","journal-title":"Appl Math Comput"},{"key":"1762_CR3","doi-asserted-by":"crossref","first-page":"1434","DOI":"10.1016\/j.ins.2009.12.016","volume":"180","author":"S Effati","year":"2010","unstructured":"Effati S, pakdaman M (2010) Artificial neural network approach for solving fuzzy differential equations. Inf Sci 180:1434\u20131457","journal-title":"Inf Sci"},{"key":"1762_CR4","unstructured":"Erdogan ME, Imrak CE (2009) An analytical solution of the Navier\u2013Stokes equation for flow over a moving plate bounded by two side walls. J Mech Eng 55(12):749\u2013754"},{"issue":"19","key":"1762_CR5","doi-asserted-by":"crossref","first-page":"2812","DOI":"10.3923\/jas.2007.2812.2817","volume":"7","author":"M Hayati","year":"2007","unstructured":"Hayati M, Karami B (2007) Feed forward neural network for solving partial differential equations. J Appl Sci 7(19):2812\u20132817","journal-title":"J Appl Sci"},{"issue":"10","key":"1762_CR6","doi-asserted-by":"crossref","first-page":"2521","DOI":"10.1002\/aic.11275","volume":"53","author":"K Horiuchi","year":"2007","unstructured":"Horiuchi K, Dutta P et al (2007) Electro osmosis with step changes in zeta potential in microchannels. AIChE J 53(10):2521\u20132533","journal-title":"AIChE J"},{"issue":"5","key":"1762_CR7","doi-asserted-by":"crossref","first-page":"987","DOI":"10.1109\/72.712178","volume":"9","author":"IE Largris","year":"1998","unstructured":"Largris IE, Likas A et al (1998) Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Netw 9(5):987\u20131000","journal-title":"IEEE Trans Neural Netw"},{"issue":"3","key":"1762_CR8","first-page":"257","volume":"24","author":"M Mohyuddin","year":"2008","unstructured":"Mohyuddin M et al (2008) Exact solutions of time-dependent Navier\u2013Stokes equations by hodograph\u2013Legendre transformation method. Tamsui Oxf J Math Sci 24(3):257\u2013268","journal-title":"Tamsui Oxf J Math Sci"},{"issue":"2","key":"1762_CR9","first-page":"97","volume":"1","author":"Z Odibat","year":"2006","unstructured":"Odibat Z, Momani S (2006) Analytical spherically symmetric solution for the time-fractional Navier\u2013Stokes equation. Adv Theor Appl Math 1(2):97\u2013107","journal-title":"Adv Theor Appl Math"},{"key":"1762_CR10","doi-asserted-by":"crossref","first-page":"056305","DOI":"10.1103\/PhysRevE.73.056305","volume":"73","author":"J Zhang","year":"2006","unstructured":"Zhang J, Liu F et al (2006) Electro-osmotic flow and mixing in heterogeneous microchannels. Phys Rev E 73:056305\u2013056312","journal-title":"Phys Rev E"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-014-1762-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-014-1762-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-014-1762-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T02:21:16Z","timestamp":1559096476000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-014-1762-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,10,30]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,5]]}},"alternative-id":["1762"],"URL":"https:\/\/doi.org\/10.1007\/s00521-014-1762-2","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,10,30]]}}}