Modified Jacobian Newton Iterative Method: Theory and Applications | Zendy

Jürgen Geiser | Zendy

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Modified Jacobian Newton Iterative Method: Theory and Applications

Author(s) -

Jürgen Geiser

Publication year - 2009

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2009/307298

Subject(s) - jacobian matrix and determinant , linearization , local convergence , iterative method , operator splitting , convergence (economics) , newton's method , nonlinear system , operator (biology) , mathematics , rate of convergence , newton's method in optimization , mathematical optimization , computer science , key (lock) , physics , biochemistry , chemistry , computer security , repressor , quantum mechanics , transcription factor , economics , gene , economic growth

This article proposes a new approach to the construction of a linearization method based on theiterative operator-splitting method for nonlinear differential equations. The convergence propertiesof such a method are studied. The main features of the proposed idea are the linearizationof nonlinear equations and the application of iterative splitting methods. We present an iterativeoperator-splitting method with embedded Newton methods to solve nonlinearity. We confirmwith numerical applications the effectiveness of the proposed iterative operator-splitting methodin comparison with the classical Newton methods. We provide improved results and convergence rates

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