Relaxing convergence conditions for Stirling's method

The aim of this paper is to study the convergence of Stirling's method used for finding fixed points of nonlinear operator equations assuming that the first Fréchet derivative of the nonlinear operator be ω‐conditioned. The ω‐condition relaxes the Lipschitz/Hölder condition on the first Fréchet...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2010-01, Vol.33 (2), p.224-232
Main Authors: Parhi, S. K., Gupta, D. K.
Format: Article
Language:English
Subjects:
Calculus of variations and optimal control
Convergence
Derivatives
Effectiveness
Exact sciences and technology
Finite differences and functional equations
Fréchet derivative
Global analysis, analysis on manifolds
Hölder condition
Integral equations
Lipschitz condition
Mathematical analysis
Mathematics
nonlinear operator equations
Nonlinearity
Operator theory
Operators
Sciences and techniques of general use
Stirling's method
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Uniqueness
ω-condition
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Summary:The aim of this paper is to study the convergence of Stirling's method used for finding fixed points of nonlinear operator equations assuming that the first Fréchet derivative of the nonlinear operator be ω‐conditioned. The ω‐condition relaxes the Lipschitz/Hölder condition on the first Fréchet derivative used earlier for the convergence. The existence and uniqueness regions are derived for the fixed points. Finally, the efficacy of our convergence analysis is shown by working out an integral equation of Hammerstein type of second kind. The results obtained show that our approach finds better results when compared with the results obtained by Newton's method. Copyright © 2009 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
1099-1476
DOI:10.1002/mma.1164