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.
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页数：16
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