Trigonometrically fitted three-derivative Runge–Kutta methods for solving oscillatory initial value problems

作者：

Highlights：

• Trigonometrically fitted three-derivative Runge–Kutta methods are proposed.

• General order conditions are derived by using the theory of the B-series.

• Some examples of explicit methods are given.

• Numerical results show the efficiency of our new methods.

摘要

•Trigonometrically fitted three-derivative Runge–Kutta methods are proposed.•General order conditions are derived by using the theory of the B-series.•Some examples of explicit methods are given.•Numerical results show the efficiency of our new methods.

论文关键词：Trigonometrically fitted methods,Three-derivative Runge–Kutta methods,Order conditions,Explicit methods,Oscillatory initial value problems

论文评审过程：Received 22 October 2017, Accepted 15 January 2018, Available online 6 March 2018, Version of Record 6 March 2018.

论文官网地址：https://doi.org/10.1016/j.amc.2018.01.017