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

作者：Moreta M J^*; Bujanda B; Jorge J C

来源：Computers & Mathematics with Applications, 2016, 71(7): 1425-1447.

DOI：10.1016/j.camwa.2016.02.015

• Fractional Step Runge-Kutta-Nystrom methods
• Second-order partial differential equations
• Order reduction
• Stability
• Consistency

We study some of the main features of Fractional Step Runge Kutta Nystrom 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.

• 出版日期2016-4