Embedded Runge-Kutta scheme for step-size control in the interaction picture method

作者：Balac Stephane^*; Mahe Fabrice

来源：Computer Physics Communications, 2013, 184(4): 1211-1219.

DOI：10.1016/j.cpc.2012.12.020

• Interaction picture method
• Embedded Runge-Kutta method
• Gross-Pitaevskii equation
• Generalised non-linear Schrodinger equation
• Split-step method

When solving certain evolution type PDEs such as the Schrodinger equation, the Interaction Picture method is a valuable alternative to Split-Step methods. The Interaction Picture method has good computational features when used together with the standard 4th order Runge-Kutta scheme (giving rise to the RK4-IP method). In this paper we present an embedded Runge-Kutta scheme with orders 3 and 4 with the aim to deliver an estimation of the local error for adaptive step-size control purposes in the Interaction Picture method. The corresponding ERK4(3)-IP method preserves the features of the RK4-IP method and provides a local error estimate at no significant extra cost.

• 出版日期2013-4