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Whirling vibration is an important part of the calculations of the design of a marine shaft. In fact, all classification societies require a propulsion shafting whirling vibration calculation giving the range of critical speeds, i.e., free whirling vibration calculation. However, whirling vibration is a source of fatigue failure of the bracket and aft stern tube bearings, destruction of high-speed shafts with universal joints, noise, and hull vibrations. There are numerous uncertainties in the calculation of whirling vibration, namely, in the shafting system modeling and in the determination of excitement and damping forces. Moreover, whirling vibration calculation mathematics is much more complex than torsional or axial calculations. The marine propulsion shaft can be studied as a selfsustained vibration system, which can be modeled using the Van der Pol equation. In this document, a new way to solve the Van der pol equation is presented. The proposed method, based on a variational approach without local minima extra to the solution, converges for whatever initial point and parameter in the Van der Pol equation.

[EN] This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. The methods have high order of convergence but only using first order derivatives. Moreover only one LU decomposition is required in each iteration. In particular, the methods are real alternatives to the classical Newton method. We present a local convergence analysis based on hypotheses only on the first derivative. These types of local results were usually proved based on hypotheses on the derivative of order higher than two although only the first derivative appears in these types of methods (Bermficlez et al., 2012; Petkovic et al., 2013; Traub, 1964). We apply these methods to an equation related to the nonlinear complementarity problem. Finally, we find the most efficient method in the family for this problem and we perform a theoretical and a numerical study for it. (C) 2018 Elsevier B.V. All rights reserved., Research was supported in part by Programa de Apoyo a Ia investigacion de Ia fundacion Seneca-Agencia de Ciencia y Tecnologia de la Region de Murcia 19374/PI/14, by the project of Generalitat Valenciana Prometeo/2016/089 and the projects MTM2015-64382-P (MINECO/FEDER), MTM2014-52016-C2-1-P and MTM2014-52016-C2-2-P of the Spanish Ministry of Science and Innovation.

In this article, an inverse free Steffensen-type method is introduced. The method is applied to approximate the systems of equations associated to implicit schemes approximating a stiff differential equation. The method has quadratic convergence without evaluating neither any derivative nor inverse operator. Finally, hypotheses ensuring the semilocal convergence and the R-order of convergence are presented.

This paper is devoted to the approximation of matrix pth roots. We present and analyze a family of algorithms free of inverses. The method is a combination of two families of iterative methods. The first one gives an approximation of the matrix inverse. The second family computes, using the first method, an approximation of the matrix pth root. We analyze the computational cost and the convergence of this family of methods. Finally, we introduce several numerical examples in order to check the performance of this combination of schemes. We conclude that the method without inverse emerges as a good alternative since a similar numerical behavior with smaller computational cost is obtained. The research of the authors S.A. and S.B. was funded in part by Programa de Apoyo a la investigación de la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18 and by PID2019-108336GB-100 (MINECO/FEDER). The research of the author M.Á.H.-V. was supported in part by Spanish MCINN PGC2018-095896-B-C21. The research of the author Á.A.M. was funded in part by Programa de Apoyo a la investigación de la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18 and by Spanish MCINN PGC2018-095896-B-C21.

The main aim of this study is to approximate the square root of matrices using an efficient iterative method. We analyse the convergence of the iterative method and the order of convergence of this kind of methods and we will apply our theoretical results to specific examples in order to prove that results.

Based on the modification of family of iterative processes of Chebyshev-Halley presented by M. Kansal et al. in [2], whose convergence is cubic, we will present in this talk a comparison between the behaviour of some members of the family in which some different means are used. We will also study the influence of that mean in the convergence of the methods.

In recent years wavelets decompositions have been widely used in computational Maxwell’s curl equations, to effectively resolve complex problems. In this paper, we review different types of wavelets that we can consider, the Cohen–Daubechies–Feauveau biorthogonal wavelets, the orthogonal Daubechies wavelets and the Deslauries–Dubuc interpolating wavelets. We summarize the main features of these frameworks and we propose some possible future works.

This paper is a small review of Chebyshev’s method. The geometric interpretation as a generalization of Newton’s method is derived. Using this interpretation its global convergence is proved. Some dynamical properties are studied. As a higher order method, they are more complicated than in Newton’s method. Finally, some applications are revisited pointing out the advantages of Chebyshev’s method with respect Newton’s method.

A generalized k-step iterative method from Steffensen’s method with frozen divided difference operator for solving a system of nonlinear equations is studied and the maximum computational efficiency is computed. Moreover, a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the method and the computational efficiency are both well deduced. By using a technique based on recurrence relations, the semilocal convergence of the family is studied. Finally, some numerical experiments related to the approximation of nonlinear elliptic equations are reported. A comparison with other derivative-free families of iterative methods is carried out.

We present a local convergence analysis of a two-point four parameter Jarratt-like method of high convergence order in order to approximate a locally unique solution of a nonlinear equation. In contrast to earlier studies such us (Amat et al. Aequat. Math. 69(3), 212---223 2015; Amat et al. J. Math. Anal. Appl. 366(3), 24---32 2010; Behl, R. 2013; Bruns and Bailey Chem. Eng. Sci. 32, 257---264 1977; Candela and Marquina. Computing 44, 169---184 1990; Candela and Marquina. Computing 45(4), 355---367 1990; Chun. Appl. Math. Comput. 190(2), 1432---1437 2007; Cordero and Torregrosa. Appl. Math. Comput. 190, 686---698 2007; Deghan. Comput. Appl Math. 29(1), 19---30 2010; Deghan. Comput. Math. Math. Phys. 51(4), 513---519 2011; Deghan and Masoud. Eng. Comput. 29(4), 356---365 15; Cordero and Torregrosa. Appl. Math. Comput. 190, 686---698 2012; Deghan and Masoud. Eng. Comput. 29(4), 356---365 2012; Ezquerro and Hernandez. Appl. Math. Optim. 41(2), 227---236 2000; Ezquerro and Hernandez. BIT Numer. Math. 49, 325---342 2009; Ezquerro and Hernandez. J. Math. Anal. Appl. 303, 591---601 2005; Gutierrez and Hernandez. Comput. Math. Appl. 36(7), 1---8 1998; Ganesh and Joshi. IMA J. Numer. Anal. 11, 21---31 1991; Gonzalez-Crespo et al. Expert Syst. Appl. 40(18), 7381---7390 2013; Hernandez. Comput. Math. Appl. 41(3-4), 433---455 2001; Hernandez and Salanova. Southwest J. Pure Appl. Math. 1, 29---40 1999; Jarratt. Math. Comput. 20(95), 434---437 1966; Kou and Li. Appl. Math. Comput. 189, 1816---1821 2007; Kou and Wang. Numer. Algor. 60, 369---390 2012; Lorenzo et al. Int. J. Interact. Multimed. Artif. Intell. 1(3), 60---66 2010; Magrenan. Appl. Math. Comput. 233, 29---38 2014; Magrenan. Appl. Math. Comput. 248, 215---224 2014; Parhi and Gupta. J. Comput. Appl. Math. 206(2), 873---887 2007; Rall 1979; Ren et al. Numer. Algor. 52(4), 585---603 2009; Rheinboldt Pol. Acad. Sci. Banach Ctr. Publ. 3, 129---142 1978; Sicilia et al. J. Comput. Appl. Math. 291, 468---477 2016; Traub 1964; Wang et al. Numer. Algor. 57, 441---456 2011) using hypotheses up to the fifth derivative, our sufficient convergence conditions involve only hypotheses on the first Frechet-derivative of the operator involved. The dynamics of the family for choices of the parameters such that it is optimal is also shown. Numerical examples are also provided in this study

The purpose of this article is to analyze the learning data set obtained from the Moodle platform andtrack student activity as an essential requirement for this new teaching-learning interactive in implementing the European Higher Educa-tion Area (EHEA) has been a substantial changes in the assessment process. The various web mining subjects used as a methodology to extract information using variables that provide information about how students interact with different activities configured in the virtual platform Moodle and monitoring that make the subject taking into temporary variables account. This is evidenced by the results that systems for managing learning, Learning Management System (LMS) in the form of virtual learning platforms store large amounts of information that can be drawn from the various subjects under interactuaciones with the virtual platform Moodle. We conclude that there is a relationship between interactions with Moodle and academic performance, and the use of students and teachers from the platform. RESUMEN El proposito de este articulo es analizar el aprendizaje a un conjunto de datos obtenidos de la plataforma Moodle y hacer seguimiento de la actividad del alumno como requerimiento imprescindible para este nuevo proceso de ensenanza-aprendizaje interactivo en la implantacion del Espacio Europeo de Ensenanza Superior (EEES), ha supuesto una modifica-cion sustancial en los procesos de evaluacion. Se utiliza como metodologia la mineria web distintas de las asignaturas para extraer informacion utilizando variables que aportan informacion acerca de la forma en la que los estudiantes interactuan con distintas actividades configuradas en la plataforma virtual Moodle, asi como el seguimiento que hacen de la asignatura teniendo en cuenta variables temporales. Se evidencia en los resultados que los sistemas para la gestion del aprendizaje, Learning Management System (LMS), en forma de plataformas virtuales de ensenanza almacenan gran cantidad de informa-cion que permiten extraer las distintas interactuaciones con asignaturas previstas en la plataforma virtual Moodle. Se con-cluye que existe relacion entre las interacciones con Moodle y el rendimiento academico, asi como el uso de los estudiantes y profesores de dicha plataforma.