{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:46:26Z","timestamp":1776843986591,"version":"3.51.2"},"publisher-location":"Berlin, Heidelberg","reference-count":12,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642041020","type":"print"},{"value":"9783642041037","type":"electronic"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-04103-7_10","type":"book-chapter","created":{"date-parts":[[2009,9,30]],"date-time":"2009-09-30T01:41:17Z","timestamp":1254274877000},"page":"94-105","source":"Crossref","is-referenced-by-count":16,"title":["Involution and Difference Schemes for the Navier\u2013Stokes Equations"],"prefix":"10.1007","author":[{"given":"Vladimir P.","family":"Gerdt","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuri A.","family":"Blinkov","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"10_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3323-5","volume-title":"Fluid Dynamics: Theory, Computation and Numerical Simulation","author":"C. Pozrikidis","year":"2001","unstructured":"Pozrikidis, C.: Fluid Dynamics: Theory, Computation and Numerical Simulation. Kluwer, Dordrecht (2001)"},{"key":"10_CR2","first-page":"51","volume":"2","author":"V.P. Gerdt","year":"2006","unstructured":"Gerdt, V.P., Blinkov, Y. A., Mozzhilkin, V.V.: Gr\u00f6bner Bases and Generation of Difference Schemes for Partial Differential Equations. SIGMA\u00a02, 51 (2006) arXiv:math.RA\/0605334","journal-title":"SIGMA"},{"key":"10_CR3","volume-title":"Partial Differential Equations and Lie Pseudogroups","author":"J.F. Pommaret","year":"1978","unstructured":"Pommaret, J.F.: Partial Differential Equations and Lie Pseudogroups. Gordon & Breach, London (1978)"},{"key":"10_CR4","first-page":"33","volume-title":"Proc. Int. Symp. Applications of Computer Algebra - ISACA 2000","author":"J. Calmet","year":"2001","unstructured":"Calmet, J., Hausdorf, M., Seiler, W.M.: A Constructive Introduction to Involution. In: Akerkar, R. (ed.) Proc. Int. Symp. Applications of Computer Algebra - ISACA 2000, pp. 33\u201350. Allied Publishers, New Delhi (2001), \n                  \n                    http:\/\/www.mathematik.uni-kassel.de\/~seiler\/"},{"key":"10_CR5","unstructured":"Janet, M.: Le\u00e7ons sur les Syst\u00e8mes d\u2019Equations aux D\u00e9riv\u00e9es Partielles. Cahiers Scientifiques, IV, Gauthier-Villars, Paris (1929)"},{"key":"10_CR6","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1016\/S0378-4754(97)00127-4","volume":"45","author":"V.P. Gerdt","year":"1998","unstructured":"Gerdt, V.P., Blinkov, Y. A.: Involutive Bases of Polynomial Ideals. Math. Comp. Sim.\u00a045, 519\u2013542 (1998) arXiv:math.AC\/9912027","journal-title":"Math. Comp. Sim."},{"key":"10_CR7","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/978-3-642-60218-4_9","volume-title":"Computer Algebra in Scientific Computing CASC 1999","author":"V.P. Gerdt","year":"1999","unstructured":"Gerdt, V.P.: Completion of Linear Differential Systems to Involution. In: Computer Algebra in Scientific Computing CASC 1999, pp. 115\u2013137. Springer, Berlin (1999) arXiv:math.AP\/9909114"},{"issue":"12","key":"10_CR8","doi-asserted-by":"publisher","first-page":"2182","DOI":"10.1063\/1.1761178","volume":"8","author":"F.H. Harlow","year":"1965","unstructured":"Harlow, F.H., Welch, J.E.: Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids\u00a08(12), 2182\u20132189 (1965)","journal-title":"Phys. Fluids"},{"key":"10_CR9","first-page":"1111","volume":"7","author":"P.M. Gresho","year":"1987","unstructured":"Gresho, P.M., Sani, R.L.: On Pressure Boundary Conditions for the Incompressible Navier-Stokes Equations. Int. J. Numer. Meth. Fluids\u00a07, 1111\u20131145 (1987)","journal-title":"Fluids"},{"key":"10_CR10","unstructured":"Sidorov, A.F., Shapeev, V.P., Yanenko, N.N.: Method of Differential Constraints and its Application to Gas Dynamics, Nauka, Novosibirsk (1984) (in Russian)"},{"key":"10_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-6947-5","volume-title":"Difference Algebra","author":"A. Levin","year":"2008","unstructured":"Levin, A.: Difference Algebra. Springer, Heidelberg (2008)"},{"key":"10_CR12","unstructured":"Davis, P.J., Rabinowitz, P.: Methods of Numerical Integration. Dover Publications (2007)"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-04103-7_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,9]],"date-time":"2019-03-09T20:45:25Z","timestamp":1552164325000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-04103-7_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642041020","9783642041037"],"references-count":12,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-04103-7_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009]]}}}