{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:14:54Z","timestamp":1760242494464,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,8,2]],"date-time":"2017-08-02T00:00:00Z","timestamp":1501632000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we extend the analysis of the Lagged Diffusivity Method for nonlinear, non-steady reaction-convection-diffusion equations. In particular, we describe how the method can be used to solve the systems arising from different discretization schemes, recalling some results on the convergence of the method itself. Moreover, we also analyze the behavior of the method in case of problems presenting boundary layers or blow-up solutions.<\/jats:p>","DOI":"10.3390\/a10030088","type":"journal-article","created":{"date-parts":[[2017,8,2]],"date-time":"2017-08-02T10:05:25Z","timestamp":1501668325000},"page":"88","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems"],"prefix":"10.3390","volume":"10","author":[{"given":"Francesco","family":"Mezzadri","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, University of Wisconsin-Madison, Madison WI 53706-1572, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emanuele","family":"Galligani","sequence":"additional","affiliation":[{"name":"Department of Engineering \u201cEnzo Ferrari\u201d, University of Modena and Reggio Emilia, via P. Vivarelli 10\/1, building 26, I-41125 Modena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,2]]},"reference":[{"key":"ref_1","unstructured":"Byrne, G., and Hall, C. (1973). The numerical solution of quasilinear elliptic equations. Numerical Solution of Systems of Nonlinear Algebraic Equations, Academic Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1080\/00207160.2012.671478","article-title":"Lagged diffusivity fixed point iteration for solving steady-state reaction diffusion problems","volume":"89","author":"Galligani","year":"2012","journal-title":"Int. J. Comp. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1016\/S0362-546X(02)00277-8","article-title":"Blow-up solutions for a class of nonlinear parabolic equations with Dirichlet boundary conditions","volume":"52","author":"Ding","year":"2003","journal-title":"Nonlinear Anal. 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The Maximum Principle, Birkhauser Verlag AG.","DOI":"10.1007\/978-3-7643-8145-5"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1016\/j.amc.2006.10.061","article-title":"Blow-up and scattering of solution for a generalized Boussinesq equation","volume":"188","author":"Wang","year":"2007","journal-title":"Appl. Math. Comp."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/S0168-9274(01)00035-6","article-title":"The Euler method in the numerical integration of reaction-diffusion problems with blow-up","volume":"38","author":"Abia","year":"2001","journal-title":"Appl. Numer. Math."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"399","DOI":"10.3934\/dcds.2002.8.399","article-title":"The problem of blow-up in nonlinear parabolic equations","volume":"8","author":"Galaktionov","year":"2002","journal-title":"Discret. Contin. Dyn. Syst."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Varga, R. (2000). 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