On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems

On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems

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 convergenc...

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Main Authors: Francesco Mezzadri, Emanuele Galligani
Format: Article
Language:English
Published: MDPI AG 2017-08-01
Series:Algorithms
Subjects:
lagged diffusivity method
diffusion equations
finite-difference discretizations
blow-up solutions
Online Access:https://www.mdpi.com/1999-4893/10/3/88
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spelling doaj-e5fd5d89b35e499a851196505c6da4672020-11-24T21:08:45ZengMDPI AGAlgorithms1999-48932017-08-011038810.3390/a10030088a10030088On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference SystemsFrancesco Mezzadri0Emanuele Galligani1Department of Mechanical Engineering, University of Wisconsin-Madison, Madison WI 53706-1572, USADepartment of Engineering “Enzo Ferrari”, University of Modena and Reggio Emilia, via P. Vivarelli 10/1, building 26, I-41125 Modena, ItalyIn 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.https://www.mdpi.com/1999-4893/10/3/88lagged diffusivity methoddiffusion equationsfinite-difference discretizationsblow-up solutions
collection DOAJ
language English
format Article
sources DOAJ
author Francesco Mezzadri
Emanuele Galligani
spellingShingle Francesco Mezzadri
Emanuele Galligani
On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems
Algorithms
lagged diffusivity method
diffusion equations
finite-difference discretizations
blow-up solutions
author_facet Francesco Mezzadri
Emanuele Galligani
author_sort Francesco Mezzadri
title On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems
title_short On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems
title_full On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems
title_fullStr On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems
title_full_unstemmed On the Lagged Diffusivity Method for the Solution of Nonlinear Finite Difference Systems
title_sort on the lagged diffusivity method for the solution of nonlinear finite difference systems
publisher MDPI AG
series Algorithms
issn 1999-4893
publishDate 2017-08-01
description 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.
topic lagged diffusivity method
diffusion equations
finite-difference discretizations
blow-up solutions
url https://www.mdpi.com/1999-4893/10/3/88
work_keys_str_mv AT francescomezzadri onthelaggeddiffusivitymethodforthesolutionofnonlinearfinitedifferencesystems
AT emanuelegalligani onthelaggeddiffusivitymethodforthesolutionofnonlinearfinitedifferencesystems
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