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Listar por palabra clave "Nonlinear equations"

Mostrando ítems 1-20 de 99

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A class of Steffensen type methods with optimal order of convergente

Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón (Elsevier, 2011-06-01)

In this paper, a family of Steffensen type methods of fourth-order convergence for solving nonlinear smooth equations is suggested. In the proposed methods, a linear combination of divided differences is used to get a ...
A consistent stable numerical scheme for a nonlinear option pricing model in illiquid markets

Company Rossi, Rafael; Jódar Sánchez, Lucas Antonio; Pintos Taronger, José Ramón (Elsevier, 2012-06)

Markets liquidity is an issue of very high concern in financial risk management. In a perfect liquid market the option pricing model becomes the well-known linear Black-Scholes problem. Nonlinear models appear when transaction ...
A convex combination approach for mean-based variants of Newton's method

Cordero Barbero, Alicia; Franceschi, Jonathan; Torregrosa Sánchez, Juan Ramón; Zagati, Anna C. (MDPI AG, 2019-09-02)

[EN] Several authors have designed variants of Newton¿s method for solving nonlinear equations by using different means. This technique involves a symmetry in the corresponding fixed-point operator. In this paper, some ...
A dynamical comparison between iterative methods with memory: Are the derivatives good for the memory?

Cordero Barbero, Alicia; Jordan-Lluch, Cristina; Torregrosa Sánchez, Juan Ramón (Elsevier, 2017)

[EN] The role of the derivatives at the iterative expression of methods with memory for solving nonlinear equations is analyzed in this manuscript. To get this aim, a known class of methods without memory is transformed ...
A family of modified Ostrowski's method with optimal eighth order of convergence

Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, María Penkova (Elsevier, 2011-12)

In this paper, we derive a new family of eighth-order methods for obtaining simple roots of nonlinear equations by using the weight function method. Each iteration of these methods requires three evaluations of the function ...
A fractional Newton method with 2 alpha th-order of convergence and its stability

Akgül, Alí; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón (Elsevier, 2019-12)

[EN] The use of fractional calculus in many branches of Science and Engineering is wide in the last years. There are different kinds of derivatives that can be useful in different problems. In this manuscript, we put the ...
A general class of four parametric with and without memory iterative methods for nonlinear equations

Zafar, Fiza; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Rafi, Aneeqa (Springer-Verlag, 2019-05)

[EN] In this paper, we have constructed a derivative-free weighted eighth-order iterative class of methods with and without-memory for solving nonlinear equations. These methods are optimal as they satisfy Kung-Traub's ...
A Higher Order Chebyshev-Halley-Type Family of Iterative Methods for Multiple Roots

Behl, Ramandeep; Martínez Molada, Eulalia; Cevallos-Alarcon, Fabricio Alfredo; Alarcon-Correa, Diego (MDPI AG, 2019-04)

[EN] The aim of this paper is to introduce new high order iterative methods for multiple roots of the nonlinear scalar equation; this is a demanding task in the area of computational mathematics and numerical analysis. ...
A Lyapunov inequality for a second order nonlinear differential equation

Almenar, P.; Jódar Sánchez, Lucas Antonio (Elsevier, 2011-04)

This paper presents a Lyapunov-type inequality for the second order nonlinear equation (r(x)y')' + p(x)f(y(x)) = 0, with r(x), p(x) > 0 and f(y) odd and positive for y > O. It also compares it with similar results. (C) ...
A multidimensional dynamical approach to iterative methods with memory

Campos, Beatriz; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vindel, Pura (Elsevier, 2015-11-15)

[EN] A dynamical approach on the dynamics of iterative methods with memory for solving nonlinear equations is made. We have designed new methods with memory from Steffensen’ or Traub’s schemes, as well as from a parametric ...
A new efficient and optimal sixteenth-order scheme for simple roots of nonlinear equations

Behl, Ramandeep; Cordero Barbero, Alicia; Motsa, Sandile S.; Torregrosa Sánchez, Juan Ramón (2017)

[EN] In this manuscript, we propose a new highly efficient and optimal scheme of order sixteen for obtaining simple roots of nonlinear equations. The derivation of this scheme is based on the rational approximation approach. ...
A new technique to obtain derivative-free optimal iterative methods for solving nonlinear equations

Cordero Barbero, Alicia; Hueso Pagoaga, José Luís; Martínez Molada, Eulalia; Torregrosa Sánchez, Juan Ramón (Elsevier, 2013-11)

A new technique to obtain derivative-free methods with optimal order of convergence in the sense of the Kung-Traub conjecture for solving nonlinear smooth equations is described. The procedure uses Steffensen-like methods ...
A note on "Convergence radius of Osada s method under Hölder continuous condition"

Hueso, J.L.; Martínez Molada, Eulalia; Gupta, D.K.; Cevallos-Alarcon, Fabricio Alfredo (Elsevier, 2018)

[EN] In this paper we revise the proofs of the results obtained in "Convergence radius of Osada's method under Holder continuous condition"[4], because the remainder of the Taylor's expansion used for the obtainment of the ...
A stable class of improved second-derivative free Chebyshev-Halley type methods with optimal eighth order convergence

Cordero Barbero, Alicia; Kansal, Munish; Kanwar, Vinay; Torregrosa Sánchez, Juan Ramón (Springer-Verlag, 2016)

[EN] In this paper, we present a uniparametric family of modified Chebyshev-Halley type methods with optimal eighth-order of convergence. In terms of computational cost, each member of the family requires only four functional ...
A stable class of modified Newton-like methods for multiple roots and their dynamics

Kansal, Munish; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Bhalla, Sonia (Walter de Gruyter GmbH, 2020-10)

[EN] There have appeared in the literature a lot of optimal eighth-order iterative methods for approximating simple zeros of nonlinear functions. Although, the similar ideas can be extended for the case of multiple zeros ...
A stable family with high order of convergence for solving nonlinear equations

Cordero Barbero, Alicia; Lotfi, Taher; Mahdiani, Katayoun; Torregrosa Sánchez, Juan Ramón (Elsevier, 2015-03-01)

[EN] Recently, Li et al. (2014) have published a new family of iterative methods, without memory, with order of convergence five or six, which are not optimal in the sense of Kung and Traub’s conjecture. Therefore, we ...
A study of the local convergence of a fifth order iterative method

Singh, Sukjith; Martínez Molada, Eulalia; Maroju, P.; Behl, Ramandeep (Springer-Verlag, 2020-06)

[EN] We present a local convergence study of a fifth order iterative method to approximate a locally unique root of nonlinear equations. The analysis is discussed under the assumption that first order Frechet derivative ...
A Variant of Chebyshev's Method with 3 alpha th-Order of Convergence by Using Fractional Derivatives

Cordero Barbero, Alicia; Girona, Ivan; Torregrosa Sánchez, Juan Ramón (MDPI AG, 2019-08-06)

[EN] In this manuscript, we propose several iterative methods for solving nonlinear equations whose common origin is the classical Chebyshev's method, using fractional derivatives in their iterative expressions. Due to the ...
Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior

Cordero Barbero, Alicia; Fardi, M.; Ghasemi, M.; Torregrosa Sánchez, Juan Ramón (Springer Verlag (Germany), 2014-03)

In this paper, we present a family of optimal, in the sense of Kung-Traub's conjecture, iterative methods for solving nonlinear equations with eighth-order convergence. Our methods are based on Chun's fourth-order method. ...
Achieving Optimal Order in a Novel Family of Numerical Methods: Insights from Convergence and Dynamical Analysis Results

Moscoso-Martínez, Marlon; Chicharro, Francisco I.; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Ureña-Callay, Gabriela (MDPI AG, 2024-07)

[EN] In this manuscript, we introduce a novel parametric family of multistep iterative methods designed to solve nonlinear equations. This family is derived from a damped Newton's scheme but includes an additional Newton ...