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Higueras Sanz, Inmaculada

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Higueras Sanz

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Inmaculada

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Ingeniería Matemática e Informática

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0000-0003-3860-3360

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288

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Subject: Time discretization ×

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    PublicationOpen Access
    Order barrier for low-storage DIRK methods with positive weights
    (Springer, 2018) Higueras Sanz, Inmaculada; Roldán Marrodán, Teodoro; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    In this paper we study an order barrier for low-storage diagonally implicit Runge-Kutta (DIRK) methods with positive weights. The Butcher matrix for these schemes, that can be implemented with only two memory registers in the van der Houwen implementation, has a special structure that restricts the number of free parameters of the method. We prove that third order low-storage DIRK methods must contain negative weights, obtaining the order barrier p ≤ 2 for these schemes. This result extends the well known one for symplectic DIRK methods, which are a particular case of low-storage DIRK methods. Some other properties of second order low-storage DIRK methods are given.
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    PublicationOpen Access
    Optimal monotonicity-preserving perturbations of a given Runge–Kutta method
    (Springer, 2018) Higueras Sanz, Inmaculada; Ketcheson, David I.; Kocsis, Tihamér A.; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    Perturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally perturb a given method in order to increase the radius of absolute monotonicity (a.m.). We prove that for methods with zero radius of a.m., it is always possible to give a perturbation with positive radius. We first study methods for linear problems and then methods for nonlinear problems. In each case, we prove upper bounds on the radius of a.m., and provide algorithms to compute optimal perturbations. We also provide optimal perturbations for many known methods.