Search results for "Fixed-point iteration"

showing 8 items of 8 documents

Trial Methods for Nonlinear Bernoulli Problem

1997

In this article we consider a free boundary problem which is related to formation of waves on a fluid surface (for example the ship waves). We study the possibility to construct ‘trial’ methods where one solves a sequence of standard flow problems formulated in different geometries that converge to the final free boundary. Furthermore, we use the shape optimization techniques to analyse the convergence of the fixed point iteration near a fixed point. For stream function case we conclude that the fast convergence can be obtained by using non-standard boundary conditions and we present numerical results to confirm the analysis.

Bernoulli's principleMathematical optimizationFlow (mathematics)Fixed-point iterationFree boundary problemApplied mathematicsBoundary (topology)Shape optimizationBoundary value problemFixed pointMathematics
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On Fixed Point (Trial) Methods for Free Boundary Problems

1992

In this note we consider the trial methods for solving steady state free boundary problems. For two test examples (electrochemical machining and continuous casting) we discuss the convergence of a fixed point method. Moreover, using the techniques of shape optimization we introduce a modification of the method, which gives us superlinear convergence rate. This is also confirmed numerically.

Continuous castingSteady state (electronics)Fixed-point iterationConvergence (routing)Applied mathematicsBoundary (topology)Shape optimizationFixed pointElectrochemical machiningMathematics
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Common fixed points in generalized metric spaces

2012

Abstract We establish some common fixed point theorems for mappings satisfying a ( ψ , φ ) -weakly contractive condition in generalized metric spaces. Presented theorems extend and generalize many existing results in the literature.

Discrete mathematicsComputational MathematicsMetric spaceFixed-point iterationSettore MAT/05 - Analisi MatematicaApplied MathematicsGeneralized metric weakly contractive condition contraction of integral type fixed point common fixed points.Common fixed pointProduct metricFixed pointIntrinsic metricMathematicsConvex metric space
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Coupled fixed point, F-invariant set and fixed point of N-order

2010

‎In this paper‎, ‎we establish some new coupled fixed point theorems in complete metric spaces‎, ‎using a new concept of $F$-invariant set‎. ‎We introduce the notion of fixed point of $N$-order as natural extension of that of coupled fixed point‎. ‎As applications‎, ‎we discuss and adapt the presented results to the setting of partially ordered cone metric spaces‎. ‎The presented results extend and complement some known existence results from the literature‎.

Discrete mathematicsCoupled fixed point F-invariant set fixed point of N-order partially ordered set cone metric spaceControl and OptimizationAlgebra and Number Theory47H10‎Fixed-point theoremFixed pointFixed-point propertyCoupled fixed point‎partially ordered setLeast fixed point‎$F$-invariant set54H25Schauder fixed point theoremFixed-point iterationSettore MAT/05 - Analisi Matematica‎34B15‎cone metric space‎fixed point of $N$-orderKakutani fixed-point theoremAnalysisHyperbolic equilibrium pointMathematics
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Common fixed points for discontinuous mappings in fuzzy metric spaces

2008

In this paper we prove some common fixed point theorems for fuzzy contraction respect to a mapping, which satisfies a condition of weak compatibility. We deduce also fixed point results for fuzzy contractive mappings in the sense of Gregori and Sapena.

Discrete mathematicsFuzzy metric spaceGeneral MathematicsFixed pointFixed-point propertyFuzzy logicFuzzy metric spaceLeast fixed pointPoints of coincidenceCommon fixed pointSettore MAT/05 - Analisi MatematicaFixed-point iterationCommon fixed pointDiscontinuous mappingCoincidence pointMathematicsRendiconti del Circolo Matematico di Palermo
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Some Common Coupled Fixed Point Results for Generalized Contraction in Complex-Valued Metric Spaces

2013

We introduce and study the notion of common coupled fixed points for a pair of mappings in complex valued metric space and demonstrate the existence and uniqueness of the common coupled fixed points in a complete complex-valued metric space in view of diverse contractive conditions. In addition, our investigations are well supported by nontrivial examples.

Discrete mathematicscoupled fixed pointArticle SubjectApplied MathematicsInjective metric spacelcsh:Mathematicscommon coupled fixed pointlcsh:QA1-939Convex metric spaceIntrinsic metricMetric spaceSettore MAT/05 - Analisi MatematicaFixed-point iterationcomplex-valued metric spaceMetric (mathematics)Contraction mappingFisher information metricMathematicsJournal of Applied Mathematics
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A Singular Multi-Grid Iteration Method for Bifurcation Problems

1984

We propose an efficient technique for the numerical computation of bifurcating branches of solutions of large sparse systems of nonlinear, parameter-dependent equations. The algorithm consists of a nested iteration procedure employing a multi-grid method for singular problems. The basic iteration scheme is related to the Lyapounov-Schmidt method and is widely used for proving the existence of bifurcating solutions. We present numerical examples which confirm the efficiency of the algorithm.

Nonlinear systemTranscritical bifurcationIterative methodPower iterationSingular solutionComputer scienceFixed-point iterationMathematicsofComputing_NUMERICALANALYSISApplied mathematicsBifurcation diagramBifurcation
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Iterative Methods for Pricing American Options under the Bates Model

2013

We consider the numerical pricing of American options under the Bates model which adds log-normally distributed jumps for the asset value to the Heston stochastic volatility model. A linear complementarity problem (LCP) is formulated where partial derivatives are discretized using finite differences and the integral resulting from the jumps is evaluated using simple quadrature. A rapidly converging fixed point iteration is described for the LCP, where each iterate requires the solution of an LCP. These are easily solved using a projected algebraic multigrid (PAMG) method. The numerical experiments demonstrate the efficiency of the proposed approach. Furthermore, they show that the PAMG meth…

ta113Mathematical optimizationStochastic volatilityDiscretizationIterative methodComputer scienceFinite difference methodLinear complementarity problemIterative methodQuadrature (mathematics)Multigrid methodFixed-point iterationBates modelLinear complementarity problemGeneral Earth and Planetary SciencesPartial derivativeAmerican optionGeneral Environmental ScienceProcedia Computer Science
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