Person: Bujanda Cirauqui, Blanca
Loading...
Email Address
person.page.identifierURI
Birth Date
Research Projects
Organizational Units
Job Title
Last Name
Bujanda Cirauqui
First Name
Blanca
person.page.departamento
Estadística, Informática y Matemáticas
person.page.instituteName
InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas
ORCID
0000-0001-7867-8805
person.page.upna
2455
Name
8 results
Search Results
Now showing 1 - 8 of 8
Publication Open Access An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions(Springer, 2022) Bujanda Cirauqui, Blanca; López García, José Luis; Pagola Martínez, Pedro Jesús; Palacios Herrero, Pablo; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe derive new convergent expansions of the symmetric standard elliptic integral RD(x,y,z), for x,y,z∈C∖(−∞,0], in terms of elementary functions. The expansions hold uniformly for large and small values of one of the three variables x, y or z (with the other two fixed). We proceed by considering a more general parametric integral from which RD(x,y,z) is a particular case. It turns out that this parametric integral is an integral representation of the Appell function F1(a;b,c;a+1;x,y). Therefore, as a byproduct, we deduce convergent expansions of F1(a;b,c;a+1;x,y). We also compute error bounds at any order of the approximation. Some numerical examples show the accuracy of the expansions and their uniform features.Publication Open Access Convergent expansions of the confluent hypergeometric functions in terms of elementary functions(American Mathematical Society, 2018) Bujanda Cirauqui, Blanca; López García, José Luis; Pagola Martínez, Pedro Jesús; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe consider the confluent hypergeometric function M(a, b; z) for z ∈ C and Rb >Ra > 0, and the confluent hypergeometric function U(a, b; z) for b ∈ C, Ra > 0, and Rz > 0. We derive two convergent expansions of M(a, b; z); one of them in terms of incomplete gamma functions γ(a, z) and another one in terms of rational functions of ez and z. We also derive a convergent expansion of U(a, b; z) in terms of incomplete gamma functions γ(a, z) and Γ(a, z). The expansions of M(a, b; z) hold uniformly in either Rz ≥ 0 or Rz ≤ 0; the expansion of U(a, b; z) holds uniformly in Rz > 0. The accuracy of the approximations is illustrated by means of some numerical experiments.Publication Open Access Avoiding the order reduction when solving second-order in time PDEs with Fractional Step Runge–Kutta–Nyström methods(Elsevier, 2016) Moreta, M. Jesús; Bujanda Cirauqui, Blanca; Jorge Ulecia, Juan Carlos; Ingeniería Matemática e Informática; Matematika eta Informatika IngeniaritzaWe study some of the main features of Fractional Step Runge–Kutta–Nyström methods when they are used to integrate Initial–Boundary Value Problems of second order in time, in combination with a suitable spatial discretization. We focus our attention on the order reduction phenomenon, which appears if classical boundary conditions are taken at the internal stages. This drawback is specially hard when time dependent boundary conditions are considered. In this paper we present an efficient technique, very simple and computationally cheap, which allows us to avoid the order reduction; such technique consists in modifying the boundary conditions for the internal stages of the method.Publication Open Access A combined fractional step domain decomposition method for the numerical integration of parabolic problems(Springer, 2004) Portero Egea, Laura; Bujanda Cirauqui, Blanca; Jorge Ulecia, Juan Carlos; Ingeniería Matemática e Informática; Matematika eta Informatika IngeniaritzaIn this paper we develop parallel numerical algorithms to solve linear time dependent coefficient parabolic problems. Such methods are obtained by means of two consecutive discretization procedures. Firstly, we realize a time integration of the original problem using a Fractional Step Runge Kutta method which provides a family of elliptic boundary value problems on certain subdomains of the original domain. Next, we discretize those elliptic problems by means of standard techniques. Using this framework, the numerical solution is obtained by solving, at each stage, a set of uncoupled linear systems of low dimension. Comparing these algorithms with the classical domain decomposition methods for parabolic problems, we obtain a reduction of computational cost because of, in this case, no Schwarz iterations are required. We give an unconditional convergence result for the totally discrete scheme and we include two numerical examples that show the behaviour of the proposed method.Publication Open Access Uniform approximations of the first symmetric elliptic integral in terms of elementary functions(Springer, 2022) Bujanda Cirauqui, Blanca; López García, José Luis; Pagola Martínez, Pedro Jesús; Palacios Herrero, Pablo; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Gobierno de Navarra / Nafarroako GobernuaWe consider the standard symmetric elliptic integral RF(x, y, z) for complex x, y, z. We derive convergent expansions of RF(x, y, z) in terms of elementary functions that hold uniformly for one of the three variables x, y or z in closed subsets (possibly unbounded) of C\ (−∞, 0]. The expansions are accompanied by error bounds. The accuracy of the expansions and their uniform features are illustrated by means of some numerical examples.Publication Open Access Convergent expansions of the incomplete gamma functions in terms of elementary functions(World Scientific Publishing, 2017) Bujanda Cirauqui, Blanca; López García, José Luis; Pagola Martínez, Pedro Jesús; Matematika eta Informatika Ingeniaritza; Institute for Advanced Materials and Mathematics - INAMAT2; Ingeniería Matemática e Informática; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaWe consider the incomplete gamma function γ(a,z) for Ra>0 and z∈C. We derive several convergent expansions of z−aγ(a,z) in terms of exponentials and rational functions of z that hold uniformly in z with Rz bounded from below. These expansions, multiplied by ez, are expansions of ezz−aγ(a,z) uniformly convergent in z with Rz bounded from above. The expansions are accompanied by realistic error bounds.Publication Open Access Aprender matemáticas con el ordenador(Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa, 2004) Bujanda Cirauqui, Blanca; Ferreira González, Chelo; Ingeniería Matemática e Informática; Matematika eta Informatika IngeniaritzaLos futuros perfiles profesionales de nuestros actuales alumnos universitarios están cambiando vertiginosamente. Uno de los grandes cambios es el que viene dado por la incorporación del ordenador a la mayoría (casi todos) de estos perfiles. Los profesionales precisan ya un alto nivel de conocimientos de informática, que en el caso más habitual es simplemente nivel de usuario, de manejo del ordenador. Por ello las nuevas tendencias de formación en la universidad deben adaptarse a estas necesidades, e incorporar al aula el ordenador, pero no como un complemento, como se ha venido haciendo hasta ahora con las clases denominadas “de prácticas”, sino como parte esencial del trabajo. Los profesores y los alumnos debemos concienciarnos de que es posible enseñar y aprender con el ordenador. Este es el propósito del libro, un curso de matemáticas básicas, con el ordenador, dirigido a alumnos de primer o primeros cursos de aquellas disciplinas donde las matemáticas no son el eje central pero sí fundamental en su formación (Empresariales, LADE, Ingenierías...). Para ello hemos seleccionado el programa Mathematica, que es el que actualmente utilizamos en la Universidad Pública de Navarra y que nos parece una potente herramienta matemática que además comprende la casi totalidad de las ramas de matemáticas. Por otro lado, este texto puede considerarse también de autoaprendizaje del programa Mathematica, puesto que es un nivel básico y no se necesitan más que los conocimientos elementales de un primer curso de matemáticas. El texto consta de seis capítulos, divididos a su vez en secciones. Los dos primeros introducen el programa y su entorno, el resto describen las opciones básicas y utilidades para un primer acercamiento al cálculo, el álgebra, los gráficos y la estadística descriptiva. Además, al final de cada sección se incluye una serie de ejercicios que recomendamos al alumno, ya que están elegidos de forma que sean un test válido del grado de asimilación de lo abordado en esa sección.Publication Embargo New fractional step Runge-Kutta-Nyström methods up to order three(Elsevier, 2020) Bujanda Cirauqui, Blanca; Moreta, M. Jesús; Jorge Ulecia, Juan Carlos; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute of Smart Cities - ISC; Estadística, Informática y MatemáticasFractional Step Runge–Kutta–Nyströ (FSRKN) methods have been revealed to be an excellent option to integrate numerically many multidimensional evolution models governed by second order in time partial differential equations. These methods, combined with suitable spatial discretizations, lead to strong computational cost reductions respect to many classical implicit time integrators. In this paper, we present the construction process of several implicit FSRKN methods of two and three levels which attain orders up to three and satisfy adequate stability properties. We have also performed some numerical experiments in order to show the unconditionally convergent behavior of these schemes as well as their computational advantages.