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.
Data di pubblicazione: | 2013 |
Titolo: | A nonlinearity lagging for the solution of nonlinear steady state reaction diffusion problems |
Autore/i: | Galligani, Emanuele |
Autore/i UNIMORE: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.cnsns.2012.07.019 |
Rivista: | |
Volume: | 18 (3) |
Pagina iniziale: | 567 |
Pagina finale: | 583 |
Codice identificativo ISI: | WOS:000310581400014 |
Codice identificativo Scopus: | 2-s2.0-84867455850 |
Citazione: | 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. |
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