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Bujanda Cirauqui, Blanca

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https://academica-e.unavarra.es/handle/2454/48757

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Bujanda Cirauqui

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Blanca

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0001-7867-8805

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2455

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2016 - 20202
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Author: Moreta, M. Jesús ×

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    PublicationOpen 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 Ingeniaritza
    We 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.
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    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 Matemáticas
    Fractional 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.