Symmetric trigonometrically-fitted two-step hybrid methods for oscillatory problems

作者：

Highlights：

• A general class of trigonometrically-fitted two-step hybrid (TFTSH) methods is proposed.

• General order conditions are derived by introducing the generalized B2-series.

• The symmetry of the new methods is investigated and the symmetric conditions are given.

• A diagonally implicit two-stage symmetric TFTSH method is given.

• Numerical results show the efficiency of our new method.

摘要

•A general class of trigonometrically-fitted two-step hybrid (TFTSH) methods is proposed.•General order conditions are derived by introducing the generalized B2-series.•The symmetry of the new methods is investigated and the symmetric conditions are given.•A diagonally implicit two-stage symmetric TFTSH method is given.•Numerical results show the efficiency of our new method.

论文关键词：Trigonometrical-fitting,Two-step hybrid methods,Oscillatory problems,Generalized B2-series,Order conditions,Symmetry

论文评审过程：Received 11 July 2017, Revised 16 May 2018, Available online 23 May 2018, Version of Record 2 June 2018.

论文官网地址：https://doi.org/10.1016/j.cam.2018.05.038