Year: 2023
Author: Yuhuan Yuan, Huazhong Tang
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 2 : pp. 305–324
Abstract
This paper continues to study the explicit two-stage fourth-order accurate time discretizations [5-7]. By introducing variable weights, we propose a class of more general explicit one-step two-stage time discretizations, which are different from the existing methods, e.g. the Euler methods, Runge-Kutta methods, and multistage multiderivative methods etc. We study the absolute stability, the stability interval, and the intersection between the imaginary axis and the absolute stability region. Our results show that our two-stage time discretizations can be fourth-order accurate conditionally, the absolute stability region of the proposed methods with some special choices of the variable weights can be larger than that of the classical explicit fourth- or fifth-order Runge-Kutta method, and the interval of absolute stability can be almost twice as much as the latter. Several numerical experiments are carried out to demonstrate the performance and accuracy as well as the stability of our proposed methods.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2201-m2020-0288
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 2 : pp. 305–324
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Multistage multiderivative methods Runge-Kutta methods Absolute stability region Interval of absolute stability.