On the Solution of a Class of Nonlinear Systems Governed by an ð ‘€ -Matrix

Woula Themistoclakis and Antonia Vecchio

Discrete Dynamics in Nature and Society, 2012, vol. 2012, 1-12

Abstract:

We consider a weakly nonlinear system of the form ( ð ¼ + 𠜑 ( ð ‘¥ ) ð ´ ) ð ‘¥ = ð ‘ , where 𠜑 ( ð ‘¥ ) is a real function of the unknown vector ð ‘¥ , and ( ð ¼ + 𠜑 ( ð ‘¥ ) ð ´ ) is an ð ‘€ -matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure ( ð ¼ + 𠜑 ( ð ‘¥ ð ‘Ÿ ) ð ´ ) ð ‘¥ ð ‘Ÿ + 1 = ð ‘ , ð ‘Ÿ = 0 , 1 , … . The global convergence is proved by considering a related fixed-point problem.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:412052

DOI: 10.1155/2012/412052

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