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Higueras Sanz, Inmaculada

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https://academica-e.unavarra.es/handle/2454/49246

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Higueras Sanz

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Inmaculada

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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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0000-0003-3860-3360

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88387

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288

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2016 - 20192
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    PublicationOpen Access
    Construction of additive semi-implicit Runge-Kutta methods with low-storage requirements
    (Springer US, 2016) Higueras Sanz, Inmaculada; Roldán Marrodán, Teodoro; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    Space discretization of some time-dependent partial differential equations gives rise to systems of ordinary differential equations in additive form whose terms have different stiffness properties. In these cases, implicit methods should be used to integrate the stiff terms while efficient explicit methods can be used for the non-stiff part of the problem. However, for systems with a large number of equations, memory storage requirement is also an important issue. When the high dimension of the problem compromises the computer memory capacity, it is important to incorporate low memory usage to some other properties of the scheme. In this paper we consider Additive Semi-Implicit Runge-Kutta (ASIRK) methods, a class of implicitexplicit Runge-Kutta methods for additive differential systems. We construct two second order 3-stage ASIRK schemes with low-storage requirements. Having in mind problems with stiffness parameters, besides accuracy and stability properties, we also impose stiff accuracy conditions. The numerical experiments done show the advantages of the new methods.
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    PublicationOpen Access
    Efficient SSP low-storage Runge-Kutta methods
    (2019) Roldán Marrodán, Teodoro; Higueras Sanz, Inmaculada; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
    In this paper we study the efficiency of Strong Stability Preserving (SSP) Runge-Kutta methods that can be implemented with a low number of registers using their Shu-Osher representation. SSP methods have been studied in the literature and stepsize restrictions that ensure numerical monotonicity have been found. However, for some problems, the observed stepsize restrictions are larger than the theoretical ones. Aiming at obtaining additional properties of the schemes that may explain their efficiency, in this paper we study the influence of the local error term in the observed stepsize restrictions. For this purpose, we consider the family of 5-stage third order SSP explicit Runge-Kutta methods, namely SSP(5,3), and the Buckley-Leverett equation. We deal with optimal SSP(5,3) schemes whose implementation requires at least 3 memory registers, and non-optimal 2-register SSP(5,3) schemes. The numerical experiments done show that small error constants improve the efficiency of the method in the sense that larger observed SSP coefficients are obtained.