Derivative-free high-order methods applied to preliminary orbit determination

From position and velocity coordinates for several given instants, it is possible to determine the orbital elements of the preliminary orbit, taking only into account mutual gravitational attraction forces between the Earth and the satellite. Nevertheless, it should be refined with later observations from ground stations, whose geographic coordinates are previously known. Different methods developed for this purpose need to find a solution of a nonlinear function. In some classical methods it is usual to employ fixed point or secant methods. The second iterative scheme is often used when it is not possible to obtain the derivative of the nonlinear function. Nowadays, there exist efficient numerical methods that are able to highly improve the results obtained by the classical schemes. We will focus our attention on the method of iteration of the true anomaly, in which the secant method is replaced by more efficient methods, such as the second-order Steffensen's method, as well as other high-order derivative-free methods. (C) 2011 Elsevier Ltd. All rights reserved.This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and by Vicerrectorado de Investigacion, Universitat Politecnica de Valencia PAID-06-2010-2285.Chicharro López, FI.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2013). Derivative-free high-order methods applied to preliminary orbit determination. Mathematical and Computer Modelling. 57(7-8):1795-1799. https://doi.org/10.1016/j.mcm.2011.11.045S17951799577-

Actualización de fármacos en epoc y asma

La EPOC es una patología caracterizada por una disminución progresiva y no reversible del flujo aéreo. El asma es una enfermedad inflamatoria de las vías respiratorias que cursa con hiperrespuesta bronquial y una obstrucción variable al flujo aéreo, total o parcialmente reversible. Los fármacos empleados para el tratamiento de estas patologías se basa fundamentalmente en el uso de: broncodilatadores inhalados, tanto de acción corta como de acción prolongada, corticoides inhalados, combinación de broncodilatador y corticoide

Increasing the order of convergence of iterative schemes for solving nonlinear systems

[EN] A set of multistep iterative methods with increasing order of convergence is presented, for solving systems of nonlinear equations. One of the main advantages of these schemes is to achieve high order of convergence with few Jacobian and functional evaluations, joint with the use of the same matrix of coefficients in the most of the linear systems involved in the process. Indeed, the application of the pseudocomposition technique on these proposed schemes allows us to increase their order of convergence, obtaining new high-order, efficient methods. Finally, some numerical tests are performed in order to check their practical behavior. (C) 2012 Elsevier B.V. All rights reserved.This research was supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02-02 and FONDOCYT 2011-1-B1-33 República DominicanaCordero Barbero, A.; Torregrosa Sánchez, JR.; Penkova Vassileva, M. (2013). Increasing the order of convergence of iterative schemes for solving nonlinear systems. Journal of Computational and Applied Mathematics. 252:86-94. https://doi.org/10.1016/j.cam.2012.11.024S869425

Bott Integrable Hamiltonian Systems on S2 x S1

In this paper, we study the topology of Bott integrable Hamiltonian flows on S2 × S1 in terms of some types of periodic orbits, called NMS periodic orbits. The set of these periodic orbits can be identified by means of some operations applied on global and local links. These operations come from the round handle decomposition of these systems on S2 × S1. We apply the results to obtain a non-integrability criterium. 1. Introduction. Let v = sgrad (H) be a hamiltonia

Approximation of artificial satellites' preliminary orbits: the efficiency challenge

In this paper the problem of the determination of the preliminary orbit of a celestial body is studied. We compare the results obtained by the classical Gauss's method with those obtained by some higher-order iterative methods for solving nonlinear equations. The original problem of the determination of the preliminary orbits was posed by means of a nonlinear equation. We modify this equation in order to obtain a nonlinear system which describes the mentioned problem and we derive a new efficient iterative method for solving it. We also propose a new definition of optimal order of convergence for iterative methods for solving nonlinear systems. © 2010 Elsevier Ltd.Supported by Ministerio de Ciencia y Tecnologia MTM2010-18539.Arroyo Martínez, V.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2011). Approximation of artificial satellites' preliminary orbits: the efficiency challenge. Mathematical and Computer Modelling. 54(7-8):1802-1807. https://doi.org/10.1016/j.mcm.2010.11.063S18021807547-

Sistematización de la experiencia de la implementación de cursos de Atención Integral de la Niñez y la Adolescencia, desarrollados por el CIES-UNAN Managua, Nicaragua, durante el período del 2008 al 2012.

Se encontró que estos cursos con su modalidad de de metodologías participativas permitió que el CIES-UNAN se ubicara como una Institución Educativa pionera en este tipo de cursos dirigidos a la Niñez menor de 6 años, por lo que se han venido dando cambios positivos en la atención que actualmente se ha venido brindando en la comunidad, y dio pauta para que se implementaran otros cursos con temas relacionados a la Atención Integral de la Niñez, por la vasta experiencia que se adquirió en sus implementaciones. Dentro de las lecciones aprendidas podemos recalcar que fue el poner en práctica los conocimientos adquiridos en salud, nutrición, participación ciudadana y estimulación temprana, así como el alto nivel de profesionalismo por parte del CIES UNAN quien sirvió como moderador entre el gobierno de turno y la universidad URACCAN comprometiéndose a la formación de los técnicos sin fines políticos orientados a la calidad de la enseñanz

Design, Analysis, and Applications of Iterative Methods for Solving Nonlinear Systems

In this chapter, we present an overview of some multipoint iterative methods for solving nonlinear systems obtained by using different techniques such as composition of known methods, weight function procedure, and pseudo-composition, etc. The dynamical study of these iterative schemes provides us valuable information about their stability and reliability. A numerical test on a specific problem coming from chemistry is performed to compare the described methods with classical ones and to confirm the theoretical results

On a Ermakov-Kalitkin scheme based family of fourth order

Cobollos, C.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2021). On a Ermakov-Kalitkin scheme based family of fourth order. Universitat Politècnica de València. 54-59. http://hdl.handle.net/10251/182972S545

Memorizing Schroder's Method as an Efficient Strategy for Estimating Roots of Unknown Multiplicity

[EN] In this paper, we propose, to the best of our knowledge, the first iterative scheme with memory for finding roots whose multiplicity is unknown existing in the literature. It improves the efficiency of a similar procedure without memory due to Schroder and can be considered as a seed to generate higher order methods with similar characteristics. Once its order of convergence is studied, its stability is analyzed showing its good properties, and it is compared numerically in terms of their basins of attraction with similar schemes without memory for finding multiple roots.This research was partially supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE).Cordero Barbero, A.; Neta, B.; Torregrosa Sánchez, JR. (2021). Memorizing Schroder's Method as an Efficient Strategy for Estimating Roots of Unknown Multiplicity. Mathematics. 9(20):1-13. https://doi.org/10.3390/math9202570S11392

Chaos and convergence of a family generalizing Homeier's method with damping parameters

[EN] In this paper, a family of parametric iterative methods for solving nonlinear equations, including Homeier's scheme, is presented. Its local convergence is obtained and the dynamical behavior on quadratic polynomials of the resulting family is studied in order to choose those values of the parameter that ensure stable behavior. To get this aim, the analysis of fixed and critical points and the associated parameter plane show the dynamical richness of the family and allow us to find members of this class with good numerical properties and also other ones with pathological conduct. To check the stable behavior of the good selected ones, the discretized planar 1D-Bratu problem is solved. Some of those chosen members of the family achieve good results when Homeier's scheme fails.This research was supported by Ministerio de Economia y Competitividad MTM2014-52016-C02-2-P.Cordero Barbero, A.; Franques, A.; Torregrosa Sánchez, JR. (2016). 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