{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T10:10:46Z","timestamp":1742983846814,"version":"3.40.3"},"publisher-location":"Cham","reference-count":18,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030410315"},{"type":"electronic","value":"9783030410322"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"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":[[2020]]},"DOI":"10.1007\/978-3-030-41032-2_13","type":"book-chapter","created":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T22:02:28Z","timestamp":1581631348000},"page":"123-130","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Weighted Time-Semidiscretization Quasilinearization Method for Solving Rihards\u2019 Equation"],"prefix":"10.1007","author":[{"given":"Miglena N.","family":"Koleva","sequence":"first","affiliation":[]},{"given":"Lubin G.","family":"Vulkov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,2,13]]},"reference":[{"key":"13_CR1","doi-asserted-by":"publisher","first-page":"424","DOI":"10.1016\/j.jcp.2014.09.031","volume":"280","author":"AA Alikhanov","year":"2015","unstructured":"Alikhanov, A.A.: A new difference scheme for the time fractional diffusion equation. J. Comput. Phys. 280, 424\u2013438 (2015)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"13_CR2","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1007\/s10596-017-9649-9","volume":"21","author":"T Arbogast","year":"2017","unstructured":"Arbogast, T., Taicher, A.L.: A cell-centered finite difference method for a denerate elliptic equation arising from two-phase mixtures. Comput. Geosci. 21(4), 700\u2013712 (2017)","journal-title":"Comput. Geosci."},{"key":"13_CR3","volume-title":"Quasilinearization and Nonlinear Boundary-Value Problems","author":"R Bellman","year":"1965","unstructured":"Bellman, R., Kalaba, R.: Quasilinearization and Nonlinear Boundary-Value Problems. Elsevier Publishing Company, New York (1965)"},{"key":"13_CR4","doi-asserted-by":"publisher","first-page":"2255","DOI":"10.1137\/100786320","volume":"32","author":"V Casulli","year":"2010","unstructured":"Casulli, V., Zanolli, P.: A nested Newton-type algorithm for finite volume methods solving Richards\u2019 equation in mixed form. SIAM J. Sci. Comput. 32, 2255\u20132273 (2010)","journal-title":"SIAM J. Sci. Comput."},{"issue":"7","key":"13_CR5","doi-asserted-by":"publisher","first-page":"1483","DOI":"10.1029\/WR026i007p01483","volume":"26","author":"M Celia","year":"1990","unstructured":"Celia, M., Boulout, F., Zarba, R.L.: A general mass-conservativ numerical solution for the unsaturated flow equation. Water Resour. Res. 26(7), 1483\u20131496 (1990)","journal-title":"Water Resour. Res."},{"issue":"4","key":"13_CR6","first-page":"413","volume":"31","author":"Y Dimitrov","year":"2017","unstructured":"Dimitrov, Y.: Three-point approximation for the Caputo fractional derivative. Commun. Appl. Math. Comput. 31(4), 413\u2013442 (2017)","journal-title":"Commun. Appl. Math. Comput."},{"key":"13_CR7","unstructured":"Evans, C., Pollock, S., Rebholz, L.G., Xiao, M.: A proof that Anderson acceleration increases the convergence rate in linearly converging fixed point methods (but not in quadratically converging ones). arXiv:1810.08455v1 [math.NA], 19 October 2018"},{"key":"13_CR8","doi-asserted-by":"publisher","first-page":"4104","DOI":"10.1088\/0022-3727\/39\/18\/022","volume":"39","author":"E Gerolymatou","year":"2006","unstructured":"Gerolymatou, E., Vardoulakis, I., Hilfer, R.: Modelling infiltration by means of a nonlinear fractional diffusion model. J. Phys. D Appl. Phys. 39, 4104\u20134110 (2006)","journal-title":"J. Phys. D Appl. Phys."},{"key":"13_CR9","unstructured":"Gerolymatou, E., Vardoulakis, I., Hilfer, R.: Simulating the saturation front using a fractional diffusion model. In: 5th GRACM International Congress on Computational Mechanics Limassol, 29 June\u20131 July 2005 (2005). https:\/\/www.icp.uni-stuttgart.de\/~hilfer\/publikationen\/pdfo\/ZZ-2005-GRACM-653.pdf"},{"key":"13_CR10","doi-asserted-by":"publisher","first-page":"892","DOI":"10.2136\/sssaj1980.03615995004400050002x","volume":"44","author":"M van Genuchten","year":"1980","unstructured":"van Genuchten, M.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892\u2013898 (1980)","journal-title":"Soil Sci. Soc. Am. J."},{"key":"13_CR11","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1016\/j.cpc.2009.11.015","volume":"181","author":"M Koleva","year":"2010","unstructured":"Koleva, M., Vulkov, L.: Two-grid quasilinearization approach to ODEs with applications to model problems in physics and mechanics. Comput. Phys. Commun. 181, 663\u2013670 (2010)","journal-title":"Comput. Phys. Commun."},{"issue":"4","key":"13_CR12","doi-asserted-by":"publisher","first-page":"1699","DOI":"10.1007\/s40314-016-0330-z","volume":"36","author":"M Koleva","year":"2017","unstructured":"Koleva, M., Vulkov, L.: Numerical solution of time-fractional Black-Scholes equation. Comput. Appl. Math. 36(4), 1699\u20131715 (2017)","journal-title":"Comput. Appl. Math."},{"key":"13_CR13","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/j.jcp.2012.09.004","volume":"239","author":"O Misiats","year":"2013","unstructured":"Misiats, O., Lipnikov, K.: Second-order accurate finite volume scheme for Richards\u2019 equation. J. Comput. Phys. 239, 125\u2013137 (2013)","journal-title":"J. Comput. Phys."},{"key":"13_CR14","doi-asserted-by":"publisher","unstructured":"Mitra, K., Pop I.S.: A modified L-scheme to solve nonlinear diffusion problems. Comput. Math. Appl. (in press). https:\/\/doi.org\/10.1016\/j.camwa.2018.09.042","DOI":"10.1016\/j.camwa.2018.09.042"},{"key":"13_CR15","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0022-1694(02)00251-2","volume":"272","author":"Y Pachepsky","year":"2003","unstructured":"Pachepsky, Y., Timlin, D., Rawls, W.: Generalized Richards\u2019 equation to simulate water transport in saturated soils. J. Hydrol. 272, 3\u201313 (2003)","journal-title":"J. Hydrol."},{"key":"13_CR16","doi-asserted-by":"publisher","unstructured":"Popova, Z., Crevoisier, D., Mailhol, J., Ruelle, P.: Assessment and simulation of water and nitrogen transfer under furrow irrigation: application of hydrus2D model to simulate nitrogen transfer. In: ICID 22nd European Regional Conference 2007, Pavia, Italy, 2\u20137 September 2007 (2007). https:\/\/doi.org\/10.13140\/2.1.1268.2242","DOI":"10.13140\/2.1.1268.2242"},{"issue":"5","key":"13_CR17","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1063\/1.1745010","volume":"1","author":"LA Richards","year":"1931","unstructured":"Richards, L.A.: Capillary conduction of liquids through porous mediums. Physics 1(5), 318\u2013333 (1931)","journal-title":"Physics"},{"key":"13_CR18","doi-asserted-by":"publisher","first-page":"664","DOI":"10.1016\/j.jcp.2010.10.011","volume":"230","author":"KS Zadeh","year":"2011","unstructured":"Zadeh, K.S.: A mass-conservative switching algorithm for modeling fluid flow in variably saturated porous media. J. Comput. Phys. 230, 664\u2013679 (2011)","journal-title":"J. Comput. Phys."}],"container-title":["Lecture Notes in Computer Science","Large-Scale Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-41032-2_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,9]],"date-time":"2020-12-09T16:24:59Z","timestamp":1607531099000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-41032-2_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030410315","9783030410322"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-41032-2_13","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"13 February 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"LSSC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Large-Scale Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Sozopol","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Bulgaria","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":"10 June 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 June 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"lssc2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/parallel.bas.bg\/Conferences\/SciCom19\/index.html","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}