An explicit trigonometrically fitted Runge–Kutta method for stiff and oscillatory problems with two frequencies. Issue 1 (1st February 2020)

• Record Type: Journal Article
• Authors: Fang, Yonglei; Yang, Yanping; You, Xiong
• Is Part Of: International journal of computer mathematics. Volume 97:Issue 1/2(2020)
• Page Start: 85
• Page End: 94
• Publication Date: 2020-02-01
• Subjects: Explicit Runge–Kutta method -- order condition -- stiff and oscillatory problem -- two-frequency trigonometrical fitting -- phase-lag; 65L04 -- 65L05 -- 65L12; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2018.1437263
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this paper, a new explicit fourth-order Runge–Kutta method adapted to oscillatory problems with two frequencies ( μ and ν ) is developed. The new method can integrate exactly the different harmonic oscillators y ′ = i μ y and y ′ = i ν y simultaneously. Numerical stability and phase properties of the new method are analysed. Numerical experiments are conducted to illustrate the high accuracy and competence of our new method in comparison with some highly effective methods from the recent literature.