Results 21 to 30 of about 2,172 (231)
A modification of the convergence conditions for Picard's iteration [PDF]
Computational & Applied Mathematics, 2004 To solve by successive approximation nonlinear equations of the form F(x)=0, where F:Ω⊆X→X, is an operator defined on an open convex domain of a Banach space X with values in X, one uses a fixed point theorem based method which requires the operator G(x)=x−F(x) to be a contraction. This has a very limited scope of applicability.
Ezquerro, J. A., Hernández, M. A.
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The Picard-HSS-SOR iteration method for absolute value equations
Journal of Inequalities and Applications, 2020 In this paper, we present the Picard-HSS-SOR iteration method for finding the solution of the absolute value equation (AVE), which is more efficient than the Picard-HSS iteration method for AVE.
Lin Zheng
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Mandelbrot Sets and Julia Sets in Picard-Mann Orbit
IEEE Access, 2020 The purpose of this paper is to introduce the Mandelbrot and Julia sets by using Picard-Mann iteration procedure. Escape criteria is established which plays an important role to generate Mandelbrot and Julia sets.
Cui Zou +4 more
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Iterative approximation of fixed points of contraction mappings in complex valued Banach spaces
Arab Journal of Mathematical Sciences, 2019 We approximate the fixed points of contraction mappings using the Picard–Krasnoselskii hybrid iterative process, which is known to converge faster than all of Picard, Mann and Ishikawa iterations in complex valued Banach spaces.
Godwin Amechi Okeke
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On numerical solution of nonlinear parabolic multicomponent diffusion-reaction problems
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 This work continues our previous analysis concerning the numerical solution of the multi-component mass transfer equations. The present test problems are two-dimensional, parabolic, non-linear, diffusion- reaction equations. An implicit finite difference
Juncu Gh., Popa C., Sarbu Gh.
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Some results on T-stability of Picard’s iteration [PDF]
SpringerPlus, 2016 We prove the existence and uniqueness of fixed points of T-stability for an iteration on partial cone metric space of Zamfirescu contraction. As an application, we prove a theorem for integral equation. We also give illustrative examples to verify our results.
Thokchom Chhatrajit, Yumnam Rohen
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A note on Picard iterates of nonexpansive mappings [PDF]
Annales Polonici Mathematici, 2001 Summary: Let \(X\) be a Banach space, \(C\) a closed subset of \(X\), and \(T:C\rightarrow C\) a nonexpansive mapping. It has recently been shown that if \(X\) is reflexive and locally uniformly convex and if the fixed point set \(F(T)\) of \(T\) has nonempty interior then the Picard iterates of the mapping \(T\) always converge to a point of \(F(T)\).
Kim, Eun Suk, Kirk, W. A.
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The Picard-Newton iteration for the Boussinesq equations
16th World Congress on Computational Mechanics and 4th Pan American Congress on Computational MechanicsWe consider the Picard-Newton and Anderson accelerated Picard-Newton solvers applied to the Boussinesq equations, nonlinear Helmholtz equations and Liouville equation, for the purpose of accelerating convergence and improving robustness with respect to ...
Hawkins, E., Rebholz, L.
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Convergence Rate of Some Two-Step Iterative Schemes in Banach Spaces
Journal of Mathematics, 2016 This article proves some theorems to approximate fixed point of Zamfirescu operators on normed spaces for some two-step iterative schemes, namely, Picard-Mann iteration, Ishikawa iteration, S-iteration, and Thianwan iteration, with their errors.
O. T. Wahab +3 more
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On C-To-R-Based Iteration Methods for a Class of Complex Symmetric Weakly Nonlinear Equations
Mathematics, 2020 To avoid solving the complex systems, we first rewrite the complex-valued nonlinear system to real-valued form (C-to-R) equivalently. Then, based on separable property of the linear and the nonlinear terms, we present a C-to-R-based Picard iteration ...
Min-Li Zeng, Guo-Feng Zhang
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