运用Newton-Cotes积分构造显式Runge-Kutta格式
CONSTRUCTING EXPLICIT RUNGE-KUTTA SCHEMES BY NEWTON-COTES INTEGRATION
阮春蕾 1徐玉倩 1董层层1
作者信息
- 1. 河南科技大学数学与统计学院,洛阳 471023
- 折叠
摘要
从Newton-Cotes积分的角度构造了一个带参数的三级二阶显式Runge-Kutta格式和两个带参数的四级三阶显式Runge-Kutta格式,给出了精度证明及稳定性条件.当参数特殊取值时,所构造的三种参数格式分别导出了常用的三阶Runge-Kutta格式(RK3)和经典的四阶Runge-Kutta 格式(RK4).通过数值算例,验证了所构造的几类Runge-Kutta格式的有效性、稳定性及高精度.与常见的各类显式Runge-Kutta格式相比,本文构造的三种Runge-Kutta格式具有更好的稳定性.
Abstract
Three explicit Runge-Kutta schemes are constructed from the viewpoint of Newton-Cotes integration,including a 3-stage 2nd order Runge-Kutta scheme with parameters and two 4-stage 3rd order Runge-Kutta schemes with parameters.The commonly used RK3 and RK4 can be obtained by taking special parameters from our schemes.The accuracy and the stability of these schemes are presented.Numerical examples are given to verify the stability,effectiveness and high accuracy of the constructed schemes.Results show that our explicit Runge-Kutta schemes have better stability than that of the classic explicit Runge-Kutta schemes.
关键词
常微分方程/Runge-Kutta法/Netwon-Cotes公式/显式/稳定性Key words
Ordinary differential equation/Runge-Kutta method/Newton-Cotes inte-gration/explict,stability引用本文复制引用
出版年
2024
NETL
NSTL
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