{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,11]],"date-time":"2024-09-11T07:58:35Z","timestamp":1726041515595},"publisher-location":"Cham","reference-count":21,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030268305"},{"type":"electronic","value":"9783030268312"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"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":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-26831-2_11","type":"book-chapter","created":{"date-parts":[[2019,8,14]],"date-time":"2019-08-14T23:07:07Z","timestamp":1565824027000},"page":"152-163","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Construction of a New Implicit Difference Scheme for 2D Boussinesq Paradigm Equation"],"prefix":"10.1007","author":[{"given":"Yu. A.","family":"Blinkov","sequence":"first","affiliation":[]},{"given":"V. P.","family":"Gerdt","sequence":"additional","affiliation":[]},{"given":"I. A.","family":"Pankratov","sequence":"additional","affiliation":[]},{"given":"E. A.","family":"Kotkova","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,7,24]]},"reference":[{"key":"11_CR1","first-page":"051","volume":"2","author":"VP 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 2, 051 (2006)","journal-title":"SIGMA"},{"key":"11_CR2","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/S0165-2125(00)00082-2","volume":"34","author":"CI Christov","year":"2001","unstructured":"Christov, C.I.: An energy - consistent Galilean - invariant dispersive shallow - water model. Wave Motion 34, 161\u2013174 (2001)","journal-title":"Wave Motion"},{"key":"11_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1007\/978-3-642-18466-6_46","volume-title":"Numerical Methods and Applications","author":"CI Christov","year":"2011","unstructured":"Christov, C.I., Kolkovska, N., Vasileva, D.: On the numerical simulation of unsteady solutions for the 2D Boussinesq paradigm equation. In: Dimov, I., Dimova, S., Kolkovska, N. (eds.) NMA 2010. LNCS, vol. 6046, pp. 386\u2013394. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-18466-6_46"},{"key":"11_CR4","doi-asserted-by":"crossref","DOI":"10.1088\/978-1-64327-047-0","volume-title":"Nonlinear Waves: Theory, Computer Simulation, Experiment","author":"MD Todorov","year":"2018","unstructured":"Todorov, M.D.: Nonlinear Waves: Theory, Computer Simulation, Experiment. Morgan & Claypool Publishers, San Rafael (2018)"},{"key":"11_CR5","doi-asserted-by":"publisher","first-page":"1039","DOI":"10.1016\/j.jcp.2013.10.015","volume":"257","author":"B Koren","year":"2014","unstructured":"Koren, B., Abgrall, R., Bochev, P., Frank, J.: Physics-compatible numerical methods. J. Comput. Phys. 257, 1039\u20131526 (2014)","journal-title":"J. Comput. Phys."},{"key":"11_CR6","volume-title":"Finite Difference Schemes and Partial Differential Equations","author":"JC Strikwerda","year":"2004","unstructured":"Strikwerda, J.C.: Finite Difference Schemes and Partial Differential Equations, 2nd edn. SIAM, Philadelphia (2004)","edition":"2"},{"key":"11_CR7","doi-asserted-by":"crossref","unstructured":"Gerdt, V.P., Robertz, D.: Consistency of finite difference approximations for linear PDE systems and its algorithmic verification. In: Watt, S.M. (ed.) ISSAC 2010, pp. 53\u201359. Association for Computing Machinery, New York (2010)","DOI":"10.1145\/1837934.1837950"},{"key":"11_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1007\/978-3-642-28212-6_3","volume-title":"Mathematical Modeling and Computational Science","author":"VP Gerdt","year":"2012","unstructured":"Gerdt, V.P.: Consistency analysis of finite difference approximations to PDE systems. In: Adam, G., Bu\u0161a, J., Hnati\u010d, M. (eds.) MMCP 2011. LNCS, vol. 7125, pp. 28\u201342. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-28212-6_3"},{"key":"11_CR9","series-title":"Algebra and Applications","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. Algebra and Applications, vol. 8. Springer, Dordrecht (2008). https:\/\/doi.org\/10.1007\/978-1-4020-6947-5"},{"key":"11_CR10","doi-asserted-by":"publisher","first-page":"1233","DOI":"10.1016\/j.jalgebra.2014.09.040","volume":"423","author":"V Gerdt","year":"2015","unstructured":"Gerdt, V., La Scala, R.: Noetherian quotients of the algebra of partial difference polynomials and Gr\u00f6bner bases of symmetric ideals. J. Algebra 423, 1233\u20131261 (2015)","journal-title":"J. Algebra"},{"key":"11_CR11","unstructured":"https:\/\/github.com\/blinkovua\/GInv\/tree\/master\/pyginv"},{"key":"11_CR12","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1007\/978-94-009-5225-6_6","volume-title":"Recent Trends in Multidimensional System","author":"B Buchberger","year":"1985","unstructured":"Buchberger, B.: Gr\u00f6bner bases: an algorithmic method in polynomial ideal theory. In: Bose, N.K. (ed.) Recent Trends in Multidimensional System, pp. 184\u2013232. Reidel, Dordrecht (1985)"},{"key":"11_CR13","doi-asserted-by":"crossref","unstructured":"Adams, W.W., Loustanau, P.: Introduction to Gr\u00f6bner Bases. Graduate Studies in Mathematics, vol. 3. American Mathematical Society (1994)","DOI":"10.1090\/gsm\/003"},{"key":"11_CR14","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-11445-3","volume-title":"Formal Algorithmic Elimination for PDEs","author":"D Robertz","year":"2014","unstructured":"Robertz, D.: Formal Algorithmic Elimination for PDEs. LNM, vol. 2121. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-11445-3"},{"key":"11_CR15","first-page":"267","volume-title":"Notes on Numerical Fluid Mechanics and Multidisciplinary Design","author":"Alina Chertock","year":"2011","unstructured":"Chertock, A., Christov, C.I., Kurganov, A: Central-upwind schemes for Boussinesq paradigm equations. In: Krause, E., Shokin, Yu., Resch, M., Kr\u00f6ner, D., Shokina, N. (eds.) Computational Science and High Performance Computing IV, vol. 115, pp. 267\u2013281 (2011)"},{"key":"11_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68983-3","volume-title":"The Method of Differential Approximation","author":"YI Shokin","year":"1983","unstructured":"Shokin, Y.I.: The Method of Differential Approximation, 1st edn. Springer, Heidelberg (1983)","edition":"1"},{"key":"11_CR17","doi-asserted-by":"publisher","DOI":"10.1002\/9781118032602","volume-title":"Computer-aided Analysis of Difference Schemes for Partial Differential Equations","author":"VG Ganzha","year":"1996","unstructured":"Ganzha, V.G., Vorozhtsov, E.V.: Computer-aided Analysis of Difference Schemes for Partial Differential Equations. Wiley, New York (1996)"},{"key":"11_CR18","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511781438","volume-title":"Fundamentals of Engineering Numerical Analysis","author":"P Moin","year":"2010","unstructured":"Moin, P.: Fundamentals of Engineering Numerical Analysis, 2nd edn. Cambridge University Press, Cambridge (2010)","edition":"2"},{"key":"11_CR19","series-title":"Algorithms and Computation in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-01287-7","volume-title":"Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra","author":"WM Seiler","year":"2010","unstructured":"Seiler, W.M.: Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra. Algorithms and Computation in Mathematics, vol. 24, 1st edn. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-01287-7","edition":"1"},{"key":"11_CR20","unstructured":"Blinkov, Yu.A., Cid, C.F., Gerdt, V.P., Plesken, W., Robertz, D.: The MAPLE package janet: II. Linear partial differential equations. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) Proceedings of the 6th International Workshop on Computer Algebra in Scientific Computing, CASC 2003, pp. 41\u201354. Technische Universit\u00e4t M\u00fcnchen (2003). Package Janet is freely available on the web page http:\/\/134.130.169.213\/Janet\/"},{"issue":"2","key":"11_CR21","first-page":"203","volume":"20","author":"VP Gerdt","year":"2012","unstructured":"Gerdt, V.P., Robertz, D.: Computation of difference Gr\u00f6bner bases. Comput. Sc. J. Moldova. 20(2), 203\u2013226 (2012). Package LDA is freely available on the web page http:\/\/134.130.169.213\/Janet\/","journal-title":"Comput. Sc. J. Moldova."}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-26831-2_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,19]],"date-time":"2023-09-19T03:48:35Z","timestamp":1695095315000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-26831-2_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030268305","9783030268312"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-26831-2_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"24 July 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CASC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Computer Algebra in Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Moscow","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Russia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 August 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30 August 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"casc2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.casc.cs.uni-bonn.de\/2019\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}