On the Explicit Two-Stage Fourth-Order Accurate Time Discretizations

On the Explicit Two-Stage Fourth-Order Accurate Time Discretizations

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.

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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.

Author Details

Yuhuan Yuan

Huazhong Tang