In this paper we consider a parametrized system of weakly nonlinear equations which corresponds to a nonlinear elliptic boundary-value problem with zero source, homogeneous boundary conditions and a positive parameter in the linear term. Positive solutions of this system are of interest to us. A characterization of this positive solution is given. Such a solution is determined by the Modified Newton-Arithmetic Mean method. This method is well suited for implementation on parallel computers. A theorem about the monotone convergence of the method is proved. An application of the method for solving a real practical problem related to the study of interacting populations is described.

A two-stage iterative method for solving a weakly nonlinear parametrized system / Galligani, Emanuele. - In: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS. - ISSN 0020-7160. - STAMPA. - 79(2002), pp. 1211-1224.

A two-stage iterative method for solving a weakly nonlinear parametrized system

GALLIGANI, Emanuele
2002

Abstract

In this paper we consider a parametrized system of weakly nonlinear equations which corresponds to a nonlinear elliptic boundary-value problem with zero source, homogeneous boundary conditions and a positive parameter in the linear term. Positive solutions of this system are of interest to us. A characterization of this positive solution is given. Such a solution is determined by the Modified Newton-Arithmetic Mean method. This method is well suited for implementation on parallel computers. A theorem about the monotone convergence of the method is proved. An application of the method for solving a real practical problem related to the study of interacting populations is described.
79
1211
1224
A two-stage iterative method for solving a weakly nonlinear parametrized system / Galligani, Emanuele. - In: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS. - ISSN 0020-7160. - STAMPA. - 79(2002), pp. 1211-1224.
Galligani, Emanuele
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/305138
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