Earth satellite dynamics by Picard iterations [PDF]
, 2022 The main effects of the Earth's oblateness on the motion of artificial satellites are usually derived from the variation of parameters equations of an average representation of the oblateness disturbing function. Rather, we approach their solution under the strict mathematical assumptions of Picard's iterative method.
Martı́n Lara
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Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators
Fixed Point Theory and Applications, 2004 In the class of quasi-contractive operators satisfying Zamfirescu's conditions, the most used fixed point iterative methods, that is, the Picard, Mann, and Ishikawa iterations, are all known to be convergent to the unique fixed point. In this paper, the
Berinde Vasile
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Constructing C0-Semigroups via Picard Iterations and Generating Functions: An Application to a Black–Scholes Integro-Differential Operator [PDF]
Mathematics, 2021 An alternative approach is proposed for constructing a strongly continuous semigroup based on the classical method of successive approximations, or Picard iterations, together with generating functions.
Marianito R. Rodrigo
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Comparison of the Rate of Convergence among Picard, Mann, Ishikawa, and Noor Iterations Applied to Quasicontractive Maps [PDF]
Fixed Point Theory and Applications, 2010 We provide sufficient conditions for Picard iteration to converge faster than Krasnoselskij, Mann, Ishikawa, or Noor iteration for quasicontractive operators.
Xue Zhiqun, Rhoades BE
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Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations
Annals of the West University of Timisoara: Mathematics and Computer Science, 2014 Two lemmas concerning the superior bound of a numerical sequence satisfying a common recurrence inequality are given. As applications, the error estimations are obtained for the Picard and Mann iterations in the case of demicontractive mappings ...
Berinde Vasile, Măruşter Ştefan
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Estimating the Local Radius of Convergence for Picard Iteration [PDF]
Algorithms, 2017 In this paper, we propose an algorithm to estimate the radius of convergence for the Picard iteration in the setting of a real Hilbert space. Numerical experiments show that the proposed algorithm provides convergence balls close to or even identical to the best ones.
Ştefan Măruşter
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Picard iterations for diffusions on symmetric matrices [PDF]
Journal of Theoretical Probability, 2015 Matrix-valued stochastic processes have been of significant importance in areas such as physics, engineering and mathematical finance. One of the first models studied has been the so-called Wishart process, which is described as the solution of a stochastic differential equation in the space of matrices.
Carlos G. Pacheco
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T-Stability of Picard Iteration in Metric Spaces [PDF]
Fixed Point Theory and Applications, 2008 AbstractWe establish a general result for the stability of Picard's iteration. Several theorems in the literature are obtained as special cases.
Qing Yuan, Β. E. Rhoades
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On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces [PDF]
Journal of Mathematics, 2020 In this research, we prove strong and weak convergence results for a class of mappings which is much more general than that of Suzuki nonexpansive mappings on Banach space through the Picard–Krasnoselskii hybrid iteration process. Using a numerical example, we prove that the Picard–Krasnoselskii hybrid iteration process converges faster than both of ...
Thabet Abdeljawad +2 more
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Convergence analysis of Suzuki's generalized nonexpansive mappings using the Picard-Abbas iteration process. [PDF]
PLoS OneNawaz B +4 more
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