Avoiding the order reduction when solving second-order in time PDEs with Fractional Step Runge-Kutta-Nyström methods

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We study some of the main features of Fractional Step Runge-Kutta-Nystr¨om 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 in 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 of modifying the boundary conditions for the internal stages of the method.
Preprint del artículo publicado en CAMWA: Article title: Avoiding the order reduction when solving second-order in time PDEs with Fractional Step Runge-Kutta-Nyström methods Article reference: CAMWA8205 Journal title: Computers and Mathematics with Applications Corresponding author: Dr. M. J. Moreta First author: Dr. M. J. Moreta Final version published online: 24-MAR-2016 Full bibliographic details: Computers and Mathematics with Applications 71 (2016), pp. 1425-1447 DOI information: 10.1016/j.camwa.2016.02.015
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