Alicia Cordero | Universidad Politécnica de Valencia (original) (raw)

Papers by Alicia Cordero

Research paper thumbnail of Artificial satellites preliminary orbit determination by the modified high-order Gauss method

International Journal of Computer Mathematics, 2012

Research paper thumbnail of Una nueva familia de métodos iterativos para ecuaciones no lineales

Research paper thumbnail of Metodos iterativos multi-punto para ecuaciones no lineales

Research paper thumbnail of On the convergence of a damped Newton-like method with modified right hand side vector

Applied Mathematics and Computation, 2015

ABSTRACT We present a convergence analysis for a damped Newton-like method with modified right-ha... more ABSTRACT We present a convergence analysis for a damped Newton-like method with modified right-hand side vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special case when the method is defined on our method provides computable error estimates based on the initial data. Such estimates were not given in relevant studies such as. Numerical examples further validating the theoretical results are also presented in this study.

Research paper thumbnail of Cadenas de órbitas periódicas en la variedad S2xS1

ABSTRACT Los flujos Morse-Smale constituyen la clase de los flujos más simples entre los estructu... more ABSTRACT Los flujos Morse-Smale constituyen la clase de los flujos más simples entre los estructuralmente estables. El estudio de este tipo de flujos, como el de otros flujos genéricos, está dirigido a su clasificación topológica. La caracterización topológica del conjunto de órbitas periódicas de un sistema Morse-Smale No Singular (en adelante, NMS), sobre la esfera S3 ha sido realizado por M. Wada. Aunque esto ha supuesto un paso muy importante en el estudio cualitativo de los sistemas NMS, la variedad sobre la que se estudia es muy restrictiva, por lo que es interesante hacer un estudio análogo sobre otras variedades tridimensionales . Dado que resultados previos de J.W. Morgan y D. Asimov asocian los centros de los toros en una descomposición en asas redondas de una variedad tridimensional con las órbitas periódicas del flujo NMS, y que cada órbita periódica de un sistema dinámico continuo sobre una variedad de dimensión tres puede considerarse como un nudo, estudiaremos la dinámica del sistema aplicando resultados de Teoría de Nudos sobre las cadenas formadas por las órbitas periódicas del flujo NMS. Por tanto, nuestro primer objetivo es obtener la descomposición en asas redondas de la variedad, encontrando todas las posibles asas ampliadas en S2xS1. A partir de esta descomposición en asas redondas de la variedad, se obtiene la caracterización topológica del conjunto de órbitas periódicas de un sistema NMS sobre S2xS1 en términos de siete operaciones sobre cadenas de órbitas periódicas con índice, cadenas y órbitas que pueden ser locales o globales en la variedad. A continuación se lleva a cabo un estudio de los flujos NMS en S2xS1 con pocas órbitas y asociado a las operaciones previamente descritas. Asimismo, se define la suma conexa de flujos sobre variedades que son, a su vez, suma conexa de las variedades sobre las que están definidos los flujos respectivos. Además, se presta especial atención al flujo NMS asociado a asas ampliadas provenientes de pegadas esenciales de asas, cuya relevancia es notoria en el caso en que S2xS1 sea espacio de fases de un sistema Hamiltoniano integrable con una integral primera no degenerada, llamada integral de Bott. S2xS1 es interesante también, desde otro punto de vista, ya que aparece como espacio de fases de sistemas Hamiltonianos Bott integrables que modelizan casos prácticos de Mecánica Celeste, tales como el problema de Dos Centros Fijos. En nuestro estudio de este problema demostramos que el espacio de fases global es, para algunos valores de la energía, la variedad S2xS1. La caracterización topológica del conjunto de órbitas periódicas obtenida previamente permite estudiar las operaciones sobre cadenas con índices que generan las cadenas de órbitas periódicas del problema de Dos Centros Fijos y el tipo de flujos a que dan lugar.

Research paper thumbnail of Damped Traub’s method: Convergence and stability

Mathematics and Computers in Simulation, 2015

Research paper thumbnail of Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure

Abstract and Applied Analysis, 2015

Research paper thumbnail of Orbital structure of the two fixed centres problem

We study the orbital structure of an integrable Hamiltonian system: the Two Fixed Centres problem... more We study the orbital structure of an integrable Hamiltonian system: the Two Fixed Centres problem, that can be considered as an approximation of the Restricted Three Body Problem (see Thirring [1978] and Charlier [1902-1907]) in the study of the motion of a material point moving inside the gravitational field generated by two stars. This approximation is also useful when the motion of an artificial satellite around a spheroidal body is considered. The knowledge of the orbital structure (type Non-Singular Morse-Smale orbits, globally and locally) of an integrable problem will allow us to transfer it to the near-integrable ones. The orbital structure has been obtained in some cases; for instance, the characterization of the set of periodic orbits of a Non-Singular Morse-Smale flow on the three-dimensional sphere has been studied and solved by M. Wada [1989], so as Casasayas et al. [1992] also obtained it for integrable hamiltonian systems in on the three-dimensional sphere. In fact, t...

Research paper thumbnail of A new parametric class of iterative methods for solving nonlinear systems

A new class of fourth-order iterative schemes for solving nonlinear equations and systems is prop... more A new class of fourth-order iterative schemes for solving nonlinear equations and systems is proposed. The convergence analysis is established, obtaining the same order of convergence for any value of the parameter. Finally, some numerical tests are made in order to check the robustness of the methods and the real dynamical behavior on specific 2-dimensional systems is analyzed, studying their stability depending on the parameter. Key words: nonlinear systems of equations, iterative methods, basins of attraction MSC 2000: 65H05, 65H10

Research paper thumbnail of Computational and Mathematical Methods in Science and Engineering Associate Editors A new parametric class of iterative methods for solving nonlinear systems

A new class of fourth-order iterative schemes for solving nonlinear equations and systems is prop... more A new class of fourth-order iterative schemes for solving nonlinear equations and systems is proposed. The convergence analysis is established, obtaining the same order of convergence for any value of the parameter. Finally, some numerical tests are made in order to check the robustness of the methods and the real dynamical behavior on specific 2-dimensional systems is analyzed, studying their stability depending on the parameter. Key words: nonlinear systems of equations, iterative methods, basins of attraction MSC 2000: 65H05, 65H10

Research paper thumbnail of 3. International Workshop on Positional Astronomy and Celestial Mechanics. Proceedings

This Workshop was included in the frame of the international agreements of the Astronomical Obser... more This Workshop was included in the frame of the international agreements of the Astronomical Observatory of Valencia University, Spain, with the Institute of Theoretical Astronomy and the Pulkovo Observatory of St. Petersburg, Russia. Contents: 1. New observational projects. 2. Instrumentation and techniques. 3. Methods of celestial mechanics. 4. Orbit determination. 5. Astrometric catalogues. 6. Peculiar objects of the Solar system. 7. Posters.

Research paper thumbnail of 3rd International Workship on Positional Astronomy and Celestial Mechanics

Research paper thumbnail of On developing fourth-order optimal families of methods for multiple roots and their dynamics

Applied Mathematics and Computation, 2015

ABSTRACT There are few optimal fourth-order methods for solving nonlinear equations when the mult... more ABSTRACT There are few optimal fourth-order methods for solving nonlinear equations when the multiplicity m of the required root is known in advance. Therefore, the first focus of this paper is on developing new fourth-order optimal families of iterative methods by a simple and elegant way. Computational and theoretical properties are fully studied along with a main theorem describing the convergence analysis. Another main focus of this paper is the dynamical analysis of the rational map associated with our proposed class for multiple roots; as far as we know, there are no deep study of this kind on iterative methods for multiple roots. Further, using Mathematica with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm the theoretical development.

Research paper thumbnail of On the local convergence of a fifth-order iterative method in Banach spaces

Applied Mathematics and Computation, 2015

ABSTRACT A new predictor–corrector iterative procedure, that combines Newton’s method as predicto... more ABSTRACT A new predictor–corrector iterative procedure, that combines Newton’s method as predictor scheme and a fifth-order iterative method as a corrector, is designed for solving nonlinear equations in Banach spaces. We analyze the local order of convergence and the regions of accessibility of the new method comparing it with Newton’s method, both theoretical and numerically.

Research paper thumbnail of Dynamics and Fractal Dimension of Steffensen-Type Methods

Research paper thumbnail of Stability of a Fourth-Order Family of Iterative Methods for Solving Nonlinear Problems

Proceedings of the Ninth International Conference on Engineering Computational Technology, 2014

Research paper thumbnail of Numerical Solution of Turbulence Problems by Solving Burgers’ Equation

Research paper thumbnail of Numerical Methods for Orbit Determination of Artificial Satellites

Proceedings of the Seventh International Conference on Engineering Computational Technology, 2010

Research paper thumbnail of Iterative Processes with High Order of Convergence for Nonlinear Systems

Proceedings of the Seventh International Conference on Engineering Computational Technology, 2010

Research paper thumbnail of Bifurcations of the roots of a 6-degree symmetric polynomial coming from the fixed point operator of a class of iterative methods

We consider the 6-degree polynomial whose roots provide the fixed points of the op-erator associa... more We consider the 6-degree polynomial whose roots provide the fixed points of the op-erator associated to the (α, c)-family of iterative methods. We analyze the bifurcations of these roots in the (α, c)-plane and we show, in the bifurcation diagrams, which are the ranges of parameters α and c for which they are real or complex.

Research paper thumbnail of Artificial satellites preliminary orbit determination by the modified high-order Gauss method

International Journal of Computer Mathematics, 2012

Research paper thumbnail of Una nueva familia de métodos iterativos para ecuaciones no lineales

Research paper thumbnail of Metodos iterativos multi-punto para ecuaciones no lineales

Research paper thumbnail of On the convergence of a damped Newton-like method with modified right hand side vector

Applied Mathematics and Computation, 2015

ABSTRACT We present a convergence analysis for a damped Newton-like method with modified right-ha... more ABSTRACT We present a convergence analysis for a damped Newton-like method with modified right-hand side vector in order to approximate a locally unique solution of a nonlinear equation in a Banach spaces setting. In the special case when the method is defined on our method provides computable error estimates based on the initial data. Such estimates were not given in relevant studies such as. Numerical examples further validating the theoretical results are also presented in this study.

Research paper thumbnail of Cadenas de órbitas periódicas en la variedad S2xS1

ABSTRACT Los flujos Morse-Smale constituyen la clase de los flujos más simples entre los estructu... more ABSTRACT Los flujos Morse-Smale constituyen la clase de los flujos más simples entre los estructuralmente estables. El estudio de este tipo de flujos, como el de otros flujos genéricos, está dirigido a su clasificación topológica. La caracterización topológica del conjunto de órbitas periódicas de un sistema Morse-Smale No Singular (en adelante, NMS), sobre la esfera S3 ha sido realizado por M. Wada. Aunque esto ha supuesto un paso muy importante en el estudio cualitativo de los sistemas NMS, la variedad sobre la que se estudia es muy restrictiva, por lo que es interesante hacer un estudio análogo sobre otras variedades tridimensionales . Dado que resultados previos de J.W. Morgan y D. Asimov asocian los centros de los toros en una descomposición en asas redondas de una variedad tridimensional con las órbitas periódicas del flujo NMS, y que cada órbita periódica de un sistema dinámico continuo sobre una variedad de dimensión tres puede considerarse como un nudo, estudiaremos la dinámica del sistema aplicando resultados de Teoría de Nudos sobre las cadenas formadas por las órbitas periódicas del flujo NMS. Por tanto, nuestro primer objetivo es obtener la descomposición en asas redondas de la variedad, encontrando todas las posibles asas ampliadas en S2xS1. A partir de esta descomposición en asas redondas de la variedad, se obtiene la caracterización topológica del conjunto de órbitas periódicas de un sistema NMS sobre S2xS1 en términos de siete operaciones sobre cadenas de órbitas periódicas con índice, cadenas y órbitas que pueden ser locales o globales en la variedad. A continuación se lleva a cabo un estudio de los flujos NMS en S2xS1 con pocas órbitas y asociado a las operaciones previamente descritas. Asimismo, se define la suma conexa de flujos sobre variedades que son, a su vez, suma conexa de las variedades sobre las que están definidos los flujos respectivos. Además, se presta especial atención al flujo NMS asociado a asas ampliadas provenientes de pegadas esenciales de asas, cuya relevancia es notoria en el caso en que S2xS1 sea espacio de fases de un sistema Hamiltoniano integrable con una integral primera no degenerada, llamada integral de Bott. S2xS1 es interesante también, desde otro punto de vista, ya que aparece como espacio de fases de sistemas Hamiltonianos Bott integrables que modelizan casos prácticos de Mecánica Celeste, tales como el problema de Dos Centros Fijos. En nuestro estudio de este problema demostramos que el espacio de fases global es, para algunos valores de la energía, la variedad S2xS1. La caracterización topológica del conjunto de órbitas periódicas obtenida previamente permite estudiar las operaciones sobre cadenas con índices que generan las cadenas de órbitas periódicas del problema de Dos Centros Fijos y el tipo de flujos a que dan lugar.

Research paper thumbnail of Damped Traub’s method: Convergence and stability

Mathematics and Computers in Simulation, 2015

Research paper thumbnail of Design of High-Order Iterative Methods for Nonlinear Systems by Using Weight Function Procedure

Abstract and Applied Analysis, 2015

Research paper thumbnail of Orbital structure of the two fixed centres problem

We study the orbital structure of an integrable Hamiltonian system: the Two Fixed Centres problem... more We study the orbital structure of an integrable Hamiltonian system: the Two Fixed Centres problem, that can be considered as an approximation of the Restricted Three Body Problem (see Thirring [1978] and Charlier [1902-1907]) in the study of the motion of a material point moving inside the gravitational field generated by two stars. This approximation is also useful when the motion of an artificial satellite around a spheroidal body is considered. The knowledge of the orbital structure (type Non-Singular Morse-Smale orbits, globally and locally) of an integrable problem will allow us to transfer it to the near-integrable ones. The orbital structure has been obtained in some cases; for instance, the characterization of the set of periodic orbits of a Non-Singular Morse-Smale flow on the three-dimensional sphere has been studied and solved by M. Wada [1989], so as Casasayas et al. [1992] also obtained it for integrable hamiltonian systems in on the three-dimensional sphere. In fact, t...

Research paper thumbnail of A new parametric class of iterative methods for solving nonlinear systems

A new class of fourth-order iterative schemes for solving nonlinear equations and systems is prop... more A new class of fourth-order iterative schemes for solving nonlinear equations and systems is proposed. The convergence analysis is established, obtaining the same order of convergence for any value of the parameter. Finally, some numerical tests are made in order to check the robustness of the methods and the real dynamical behavior on specific 2-dimensional systems is analyzed, studying their stability depending on the parameter. Key words: nonlinear systems of equations, iterative methods, basins of attraction MSC 2000: 65H05, 65H10

Research paper thumbnail of Computational and Mathematical Methods in Science and Engineering Associate Editors A new parametric class of iterative methods for solving nonlinear systems

A new class of fourth-order iterative schemes for solving nonlinear equations and systems is prop... more A new class of fourth-order iterative schemes for solving nonlinear equations and systems is proposed. The convergence analysis is established, obtaining the same order of convergence for any value of the parameter. Finally, some numerical tests are made in order to check the robustness of the methods and the real dynamical behavior on specific 2-dimensional systems is analyzed, studying their stability depending on the parameter. Key words: nonlinear systems of equations, iterative methods, basins of attraction MSC 2000: 65H05, 65H10

Research paper thumbnail of 3. International Workshop on Positional Astronomy and Celestial Mechanics. Proceedings

This Workshop was included in the frame of the international agreements of the Astronomical Obser... more This Workshop was included in the frame of the international agreements of the Astronomical Observatory of Valencia University, Spain, with the Institute of Theoretical Astronomy and the Pulkovo Observatory of St. Petersburg, Russia. Contents: 1. New observational projects. 2. Instrumentation and techniques. 3. Methods of celestial mechanics. 4. Orbit determination. 5. Astrometric catalogues. 6. Peculiar objects of the Solar system. 7. Posters.

Research paper thumbnail of 3rd International Workship on Positional Astronomy and Celestial Mechanics

Research paper thumbnail of On developing fourth-order optimal families of methods for multiple roots and their dynamics

Applied Mathematics and Computation, 2015

ABSTRACT There are few optimal fourth-order methods for solving nonlinear equations when the mult... more ABSTRACT There are few optimal fourth-order methods for solving nonlinear equations when the multiplicity m of the required root is known in advance. Therefore, the first focus of this paper is on developing new fourth-order optimal families of iterative methods by a simple and elegant way. Computational and theoretical properties are fully studied along with a main theorem describing the convergence analysis. Another main focus of this paper is the dynamical analysis of the rational map associated with our proposed class for multiple roots; as far as we know, there are no deep study of this kind on iterative methods for multiple roots. Further, using Mathematica with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm the theoretical development.

Research paper thumbnail of On the local convergence of a fifth-order iterative method in Banach spaces

Applied Mathematics and Computation, 2015

ABSTRACT A new predictor–corrector iterative procedure, that combines Newton’s method as predicto... more ABSTRACT A new predictor–corrector iterative procedure, that combines Newton’s method as predictor scheme and a fifth-order iterative method as a corrector, is designed for solving nonlinear equations in Banach spaces. We analyze the local order of convergence and the regions of accessibility of the new method comparing it with Newton’s method, both theoretical and numerically.

Research paper thumbnail of Dynamics and Fractal Dimension of Steffensen-Type Methods

Research paper thumbnail of Stability of a Fourth-Order Family of Iterative Methods for Solving Nonlinear Problems

Proceedings of the Ninth International Conference on Engineering Computational Technology, 2014

Research paper thumbnail of Numerical Solution of Turbulence Problems by Solving Burgers’ Equation

Research paper thumbnail of Numerical Methods for Orbit Determination of Artificial Satellites

Proceedings of the Seventh International Conference on Engineering Computational Technology, 2010

Research paper thumbnail of Iterative Processes with High Order of Convergence for Nonlinear Systems

Proceedings of the Seventh International Conference on Engineering Computational Technology, 2010

Research paper thumbnail of Bifurcations of the roots of a 6-degree symmetric polynomial coming from the fixed point operator of a class of iterative methods

We consider the 6-degree polynomial whose roots provide the fixed points of the op-erator associa... more We consider the 6-degree polynomial whose roots provide the fixed points of the op-erator associated to the (α, c)-family of iterative methods. We analyze the bifurcations of these roots in the (α, c)-plane and we show, in the bifurcation diagrams, which are the ranges of parameters α and c for which they are real or complex.