Exponentially fitted two-derivative DIRK methods for oscillatory differential equations
作者：
Highlights：
• New order conditions for EFTDDIRK methods up to order 6 are derived using bi-colored rooted trees and a novel definition of elementary weight function.
• Exponential fitting conditions for the reference sets of any order involving sin(x) and cos(x) for the new EFTDDIRK methods were derived.
• The first ever 2-stage 5th-order exponentially fitted two-derivative of Runge–Kuttatype is constructed.
• A family of 2-stage 4th-order EFTDDIRK methods with optimized phase-lag property is constructed, A 3-stage sixth-order method is also constructed.
• Numerical experiments have confirmed clearly the high efficiency of the new EFTDDIRK methods.
摘要
•New order conditions for EFTDDIRK methods up to order 6 are derived using bi-colored rooted trees and a novel definition of elementary weight function.•Exponential fitting conditions for the reference sets of any order involving sin(x) and cos(x) for the new EFTDDIRK methods were derived.•The first ever 2-stage 5th-order exponentially fitted two-derivative of Runge–Kuttatype is constructed.•A family of 2-stage 4th-order EFTDDIRK methods with optimized phase-lag property is constructed, A 3-stage sixth-order method is also constructed.•Numerical experiments have confirmed clearly the high efficiency of the new EFTDDIRK methods.
论文关键词：Exponential/trigonometrical fitting,Two-derivative Runge–Kutta methods,Diagonally implicit methods,Oscillatory differential equations
论文评审过程：Received 29 December 2020, Revised 26 October 2021, Accepted 30 October 2021, Available online 28 November 2021, Version of Record 28 November 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126770
