Two-Derivative Runge–Kutta Methods with Frequency Dependent Coefficients for Solving Orbital or Oscillatory Problems
Year: 2025
Type: article
Abstract: In this work, explicit Two-Derivative Runge–Kutta methods of the general case (that use several evaluations of the right-hand side function and its derivative per step) are considered. In order to address problems of orbital or oscillatory character, we develop methods with frequency-dependent coefficients. We construct three exponentially/trigonometrically fitted methods following two approaches suggested by Vanden Berghe and Simos. Also, we construct a phase-fitted and amplification-fitted method. The efficiency of the new modified methods is demonstrated by numerical examples.
Source: Algorithms
DOI: 10.3390/a18100603
Institution: University of Western Macedonia
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,930
OpenAlex ID: W4414545463