Order reduction and how to avoid it when explicit Runge–Kutta–Nyström methods are used to solve linear partial differential equations

Abstract

In this paper, we study the order reduction which turns up when explicit Runge–Kutta–Nyström methods are used to discretize linear second order hyperbolic equations by means of the method of lines. The order observed in practice, including its fractional part, is obtained. It is also proved that the order reduction can be completely avoided taking the boundary values of the intermediate stages of the time semidiscretization. The numerical experiments confirm that the optimal order can be reached.