This paper concerns with the analysis of the iterative procedure for the solution of a nonlinear reaction diffusion equation at the steady state in a two dimensional bounded domain supplemented by suitable boundary conditions. This procedure, called Lagged Diffusivity Functional Iteration (LDFI)-procedure, computes the solution by "lagging'' the diffusion term. A model problem is considered and a finite difference discretization for that model problem is described.Furthermore, properties of the finite difference operator are proved. Then, sufficient conditions for the convergence of the LDFI-procedure are given. At each stage of the LDFI-procedure a weakly nonlinearalgebraic system has to be solved and the simplified Newton-Arithmetic Mean method is used. This method is particularly well suited for implementation on parallel computers.Numerical studies show the efficiency, for different test functions, of the LDFI-procedure combined with the simplified Newton-Arithmetic Mean method. Better results are obtained when in the reaction diffusion equation also a convection term is present.

A nonlinearity lagging for the solution of nonlinear steady state reaction diffusion problems / Galligani, Emanuele. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - STAMPA. - 18:3(2013), pp. 567-583. [10.1016/j.cnsns.2012.07.019]

### A nonlinearity lagging for the solution of nonlinear steady state reaction diffusion problems

#### Abstract

This paper concerns with the analysis of the iterative procedure for the solution of a nonlinear reaction diffusion equation at the steady state in a two dimensional bounded domain supplemented by suitable boundary conditions. This procedure, called Lagged Diffusivity Functional Iteration (LDFI)-procedure, computes the solution by "lagging'' the diffusion term. A model problem is considered and a finite difference discretization for that model problem is described.Furthermore, properties of the finite difference operator are proved. Then, sufficient conditions for the convergence of the LDFI-procedure are given. At each stage of the LDFI-procedure a weakly nonlinearalgebraic system has to be solved and the simplified Newton-Arithmetic Mean method is used. This method is particularly well suited for implementation on parallel computers.Numerical studies show the efficiency, for different test functions, of the LDFI-procedure combined with the simplified Newton-Arithmetic Mean method. Better results are obtained when in the reaction diffusion equation also a convection term is present.
##### Scheda breve Scheda completa Scheda completa (DC)
2013
18
3
567
583
A nonlinearity lagging for the solution of nonlinear steady state reaction diffusion problems / Galligani, Emanuele. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - STAMPA. - 18:3(2013), pp. 567-583. [10.1016/j.cnsns.2012.07.019]
Galligani, Emanuele
File in questo prodotto:
File
CNSNS-2013.pdf

Open access

Descrizione: Articolo principale
Tipologia: Versione dell'autore revisionata e accettata per la pubblicazione
Dimensione 414.29 kB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/754249`