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Volume 41, Issue 2
On the Explicit Two-Stage Fourth-Order Accurate Time Discretizations

Yuhuan Yuan & Huazhong Tang

DOI: 10.4208/jcm.2201-m2020-0288

J. Comp. Math., 41 (2023), pp. 305-324.

Published online: 2022-11

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  • 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.

  • Keywords

Multistage multiderivative methods, Runge-Kutta methods, Absolute stability region, Interval of absolute stability.

  • AMS Subject Headings

65L05, 65L06, 65L20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

1548602562@qq.com (Yuhuan Yuan)

hztang@math.pku.edu.cn (Huazhong Tang)

  • BibTex
  • RIS
  • TXT
@Article{JCM-41-305, author = {Yuan , Yuhuan and Tang , Huazhong}, title = {On the Explicit Two-Stage Fourth-Order Accurate Time Discretizations}, journal = {Journal of Computational Mathematics}, year = {2022}, volume = {41}, number = {2}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2201-m2020-0288}, url = {http://global-sci.org/intro/article_detail/jcm/21182.html} }
TY - JOUR T1 - On the Explicit Two-Stage Fourth-Order Accurate Time Discretizations AU - Yuan , Yuhuan AU - Tang , Huazhong JO - Journal of Computational Mathematics VL - 2 SP - 305 EP - 324 PY - 2022 DA - 2022/11 SN - 41 DO - http://doi.org/10.4208/jcm.2201-m2020-0288 UR - https://global-sci.org/intro/article_detail/jcm/21182.html KW - Multistage multiderivative methods, Runge-Kutta methods, Absolute stability region, Interval of absolute stability. AB -

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.

Yuan , Yuhuan and Tang , Huazhong. (2022). On the Explicit Two-Stage Fourth-Order Accurate Time Discretizations. Journal of Computational Mathematics. 41 (2). 305-324. doi:10.4208/jcm.2201-m2020-0288
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