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

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Moreta Santos, María Jesús and Bujanda, Blanca and Jorge, Juan Carlos (2016) Avoiding the order reduction when solving second-order in time PDEs with Fractional Step Runge-Kutta-Nyström methods. Computers and mathematics with applications, 71 . pp. 1425-1447. ISSN 0898-1221

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Official URL: https://doi.org/10.1016/j.camwa.2016.02.015



Abstract

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.


Item Type:Article
Additional Information:

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

Uncontrolled Keywords:Fractional Step Runge-Kutta-Nystr¨om methods; Second-order partial differential equations; Order reduction; Stability; Consistency.
Subjects:Sciences > Mathematics
ID Code:43936
Deposited On:12 Sep 2017 08:46
Last Modified:12 Sep 2017 12:05

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