{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T05:17:03Z","timestamp":1721798223394},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,8,6]],"date-time":"2020-08-06T00:00:00Z","timestamp":1596672000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,6]],"date-time":"2020-08-06T00:00:00Z","timestamp":1596672000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s40314-020-01282-9","type":"journal-article","created":{"date-parts":[[2020,8,6]],"date-time":"2020-08-06T14:02:47Z","timestamp":1596722567000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Numerical solutions in chromatography using large time step and overlapping grids methods"],"prefix":"10.1007","volume":"39","author":[{"given":"Ilija","family":"Jegdi\u0107","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,8,6]]},"reference":[{"issue":"3","key":"1282_CR1","doi-asserted-by":"publisher","first-page":"893","DOI":"10.1137\/S0036142902405394","volume":"41","author":"MJ Berger","year":"2003","unstructured":"Berger MJ, Helzel C, LeVeque RJ (2003) $$h$$-box methods for the approximation of hyperbolic conservation laws on irregular grids. SIAM J Numer Anal 41(3):893\u2013918","journal-title":"SIAM J Numer Anal"},{"key":"1282_CR2","unstructured":"Bressan A (2009) Lecture notes on hyperbolic conservation laws. http:\/\/php.math.unifi.it\/users\/cimeCourses\/2009\/01\/200912-Notes.pdf. Assessed 1 May 2019"},{"key":"1282_CR3","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1090\/S0025-5718-1981-0606500-X","volume":"36","author":"B Enqquist","year":"1981","unstructured":"Enqquist B, Osher S (1981) One sided difference approximation for nonlinear conservation laws. Math Comput 36:321\u2013351","journal-title":"Math Comput"},{"key":"1282_CR4","unstructured":"Godlewski E, Raviart PA (1991) Hyperbolic systems of conservation laws. Math Appl"},{"key":"1282_CR5","first-page":"271","volume":"47","author":"SK Godunov","year":"1959","unstructured":"Godunov SK (1959) A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics. Math Sb 47:271\u2013290","journal-title":"Math Sb"},{"key":"1282_CR6","unstructured":"Jegdi\u0107 I (2014) Large time step and overlapping grids for conservation laws. Dissertation, University of Houston"},{"issue":"2","key":"1282_CR7","first-page":"1110","volume":"13","author":"I Jegdi\u0107","year":"2018","unstructured":"Jegdi\u0107 I (2018) Numerical study of singular and delta shock solutions using a large time step method. Appl Appl Math 13(2):1110\u20131122","journal-title":"Appl Appl Math"},{"issue":"4","key":"1282_CR8","first-page":"452","volume":"49","author":"I Jegdi\u0107","year":"2019","unstructured":"Jegdi\u0107 I (2019) Transitional shock waves using overlapping grids methods. IAENG Int J Appl Math 49(4):452\u2013458","journal-title":"IAENG Int J Appl Math"},{"key":"1282_CR9","unstructured":"Jegdi\u0107 I, Sanders R (2020) Large time step method for multidimensional conservation laws (in preparation)"},{"key":"1282_CR10","doi-asserted-by":"crossref","unstructured":"Keyfitz BL, Kranzer HC (1989) A viscous approximation to a system of conservation laws with no classical Riemann solution. In: Carasso C (ed) Nonlinear hyperbolic problems, lecture notes in mathematics. Springer, Berlin, pp 185\u2013197","DOI":"10.1007\/BFb0083875"},{"key":"1282_CR11","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1006\/jdeq.1995.1080","volume":"118","author":"BL Keyfitz","year":"1995","unstructured":"Keyfitz BL, Kranzer HC (1995) Spaces of weighted measures for conservation laws with singular shock solutions. J Differ Equ 118:420\u2013451","journal-title":"J Differ Equ"},{"key":"1282_CR12","doi-asserted-by":"crossref","unstructured":"Lax PD (1973) Hyperbolic systems of conservation laws and the mathematical theory of shock waves. CBMS Regional Conference Series in Mathematics No. 11. SIAM, Philadelphia","DOI":"10.1137\/1.9781611970562"},{"key":"1282_CR13","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1002\/cpa.3160130205","volume":"13","author":"PD Lax","year":"1960","unstructured":"Lax PD, Wendroff B (1960) Systems of conservation laws. Commun Pure Appl Math 13:217\u2013237","journal-title":"Commun Pure Appl Math"},{"key":"1282_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-5116-9","volume-title":"Numerical methods for conservation laws","author":"R LeVeque","year":"1990","unstructured":"LeVeque R (1990) Numerical methods for conservation laws. Birkhauser, Boston"},{"key":"1282_CR15","doi-asserted-by":"publisher","first-page":"7733","DOI":"10.1021\/ie9001537","volume":"48","author":"M Mazzotti","year":"2009","unstructured":"Mazzotti M (2009) Non-classical composition fronts in nonlinear chromatography\u2014delta shock. Ind Eng Chem Res 48:7733\u20137752","journal-title":"Ind Eng Chem Res"},{"issue":"13","key":"1282_CR16","doi-asserted-by":"publisher","first-page":"2002","DOI":"10.1016\/j.chroma.2010.01.059","volume":"1217","author":"M Mazzotti","year":"2010","unstructured":"Mazzotti M, Tarafder A, Cornel J, Gritti F, Guiochon G (2010) Experimental evidence of a delta-shock in nonlinear chromatography. J Chromatogr A 1217(13):2002\u20132012","journal-title":"J Chromatogr A"},{"key":"1282_CR17","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1090\/S0033-569X-08-01109-5","volume":"66","author":"M Nedeljkov","year":"2008","unstructured":"Nedeljkov M (2008) Singular shock waves in interactions. Q Appl Math 66:281\u2013302","journal-title":"Q Appl Math"},{"key":"1282_CR18","volume-title":"First order partial differential equations","author":"HK Rhee","year":"1986","unstructured":"Rhee HK, Aris R, Amundson NR (1986) First order partial differential equations, vol I. Prentice-Hall, Englewood Cliffs"},{"key":"1282_CR19","volume-title":"First order partial differential equations","author":"HK Rhee","year":"1989","unstructured":"Rhee HK, Aris R, Amundson NR (1989) First order partial differential equations, vol II. Prentice-Hall, Englewood Cliffs"},{"key":"1282_CR20","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1016\/0021-9991(81)90128-5","volume":"43","author":"PL Roe","year":"1981","unstructured":"Roe PL (1981) Approximate Riemann solvers, parameter vectors and difference schemes. J Comput Phys 43:357\u2013372","journal-title":"J Comput Phys"},{"key":"1282_CR21","first-page":"39","volume":"38","author":"R Sanders","year":"2007","unstructured":"Sanders R (2007) An introduction to the finite volume method for the equations of gas dynamics. SeMA J Soc Esp Mat Apl 38:39\u201368","journal-title":"SeMA J Soc Esp Mat Apl"},{"issue":"88","key":"1282_CR22","first-page":"1","volume":"190","author":"M Sever","year":"2007","unstructured":"Sever M (2007) Distribution solutions of nonlinear systems of conservation laws. Mem Am Math Soc 190(88):1\u2013163","journal-title":"Mem Am Math Soc"},{"key":"1282_CR23","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1016\/j.jde.2006.08.003","volume":"231","author":"VM Shelkovich","year":"2006","unstructured":"Shelkovich VM (2006) The Riemann problem admitting $$\\delta $$-, $$\\delta ^{\\prime }$$-shocks and vacuum states (the vanishing viscosity approach). J Differ Equ 231:459\u2013500","journal-title":"J Differ Equ"},{"key":"1282_CR24","doi-asserted-by":"crossref","unstructured":"Smoller J (1994) Shock waves and reaction-diffusion equations. Springer Science + Business Media, LLC","DOI":"10.1007\/978-1-4612-0873-0"},{"key":"1282_CR25","doi-asserted-by":"crossref","unstructured":"Sun M (2011) Delta shock waves for the chromatography equations as self-similar viscosity limits. Q Appl Math LXIX(3):425\u2013443","DOI":"10.1090\/S0033-569X-2011-01207-3"},{"key":"1282_CR26","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1016\/j.aml.2013.01.002","volume":"26","author":"M Sun","year":"2013","unstructured":"Sun M (2013) Interactions of delta shock waves for the chromatography equations. Appl Math Lett 26:631\u2013637","journal-title":"Appl Math Lett"},{"issue":"2","key":"1282_CR27","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1016\/j.jmaa.2016.03.001","volume":"239","author":"C Tsikkou","year":"2016","unstructured":"Tsikkou C (2016) Singular shocks in a chromatography model. J Math Anal Appl 239(2):766\u2013797","journal-title":"J Math Anal Appl"},{"key":"1282_CR28","doi-asserted-by":"publisher","first-page":"1451","DOI":"10.1007\/s00033-013-0300-x","volume":"64","author":"G Wang","year":"2013","unstructured":"Wang G (2013) One-dimensional nonlinear chromatography system and delta-shock waves. Z Angew Math Phys 64:1451\u20131469","journal-title":"Z Angew Math Phys"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01282-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-020-01282-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01282-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,5]],"date-time":"2021-08-05T23:16:30Z","timestamp":1628205390000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-020-01282-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,6]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["1282"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01282-9","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,6]]},"assertion":[{"value":"9 March 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 June 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 July 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with ethical standards"}},{"value":"The author has no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"235"}}