Jorge Ulecia, Juan Carlos

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https://academica-e.unavarra.es/handle/2454/49326

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Jorge Ulecia

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Juan Carlos

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Estadística, Informática y Matemáticas

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ISC. Institute of Smart Cities

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0000-0001-5906-6125

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88437

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476

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2016 - 20182
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Author: Jorge Ulecia, Juan Carlos × Subject: Order reduction ×

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Now showing 1 - 2 of 2
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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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    PublicationOpen Access
    An efficient numerical method for singularly perturbed time dependent parabolic 2D convection-diffusion systems
    (Elsevier, 2018) Clavero, Carmelo; Jorge Ulecia, Juan Carlos; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Institute of Smart Cities - ISC
    In this paper we deal with solving efficiently 2D linear parabolic singularly perturbed systems of convection–diffusion type. We analyze only the case of a system of two equations where both of them feature the same diffusion parameter. Nevertheless, the method is easily extended to systems with an arbitrary number of equations which have the same diffusion coefficient. The fully discrete numerical method combines the upwind finite difference scheme, to discretize in space, and the fractional implicit Euler method, together with a splitting by directions and components of the reaction–convection–diffusion operator, to discretize in time. Then, if the spatial discretization is defined on an appropriate piecewise uniform Shishkin type mesh, the method is uniformly convergent and it is first order in time and almost first order in space. The use of a fractional step method in combination with the splitting technique to discretize in time, means that only tridiagonal linear systems must be solved at each time level of the discretization. Moreover, we study the order reduction phenomenon associated with the time dependent boundary conditions and we provide a simple way of avoiding it. Some numerical results, which corroborate the theoretical established properties of the method, are shown.