Derivation of Three-Derivative Two-Step Runge-Kutta Methods

被引：2
|
作者：
Qin, Xueyu [1 ,2 ]
Yu, Jian [1 ,2 ]
Yan, Chao [1 ,2 ]
机构：
[1] Beihang Univ, Natl Key Lab Computat Fluid Dynam, Beijing 100191, Peoples R China
[2] Beihang Univ, Sch Aeronaut Sci & Engn, Beijing 100191, Peoples R China
来源：
MATHEMATICS | 2024年 / 12卷 / 05期
关键词：
multiderivative methods; two-step Runge-Kutta methods; A-stability property; order conditions; HIGH-ORDER;
D O I：
10.3390/math12050711
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we develop explicit three-derivative two-step Runge-Kutta (ThDTSRK) schemes, and propose a simpler general form of the order accuracy conditions (p <= 7) by Albrecht's approach, compared to the order conditions in terms of rooted trees. The parameters of the general high-order ThDTSRK methods are determined by utilizing the order conditions. We establish a theory for the A-stability property of ThDTSRK methods and identify optimal stability coefficients. Moreover, ThDTSRK methods can achieve the intended order of convergence using fewer stages than other schemes, making them cost-effective for solving the ordinary differential equations.
引用
收藏
页数：16
相关论文
共 50 条
  • [21] Two-step Runge-Kutta methods for stochastic differential equations
    D'Ambrosio, Raffaele
    Scalone, Carmela
    APPLIED MATHEMATICS AND COMPUTATION, 2021, 403
  • [22] A simple technique for constructing two-step Runge-Kutta methods
    L. M. Skvortsov
    Computational Mathematics and Mathematical Physics, 2009, 49 : 1837 - 1846
  • [23] Two-step Runge-Kutta Methods with Quadratic Stability Functions
    Conte, D.
    D'Ambrosio, R.
    Jackiewicz, Z.
    JOURNAL OF SCIENTIFIC COMPUTING, 2010, 44 (02) : 191 - 218
  • [24] Trigonometrically fitted three-derivative Runge-Kutta methods for solving oscillatory initial value problems
    Li, Jiyong
    APPLIED MATHEMATICS AND COMPUTATION, 2018, 330 : 103 - 117
  • [25] Nested Second Derivative Two-Step Runge–Kutta Methods
    Olatunji P.O.
    Ikhile M.N.O.
    Okuonghae R.I.
    International Journal of Applied and Computational Mathematics, 2021, 7 (6)
  • [26] Two-step Runge-Kutta: Theory and practice
    Tracogna, S
    Welfert, B
    BIT, 2000, 40 (04): : 775 - 799
  • [27] A Class of Two-Derivative Two-Step Runge-Kutta Methods for Non-Stiff ODEs
    Aiguobasimwin, I. B.
    Okuonghae, R. I.
    JOURNAL OF APPLIED MATHEMATICS, 2019, 2019
  • [28] Two-Step Runge-Kutta: Theory and Practice
    S. Tracogna
    B. Welfert
    BIT Numerical Mathematics, 2000, 40 : 775 - 799
  • [29] On explicit two-derivative two-step Runge–Kutta methods
    Mukaddes Ökten Turaci
    Turgut Öziş
    Computational and Applied Mathematics, 2018, 37 : 6920 - 6954
  • [30] A CLASS OF IMPLICIT-EXPLICIT TWO-STEP RUNGE-KUTTA METHODS
    Zharovsky, Evgeniy
    Sandu, Adrian
    Zhang, Hong
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2015, 53 (01) : 321 - 341
12345