Dormand 和 Prince 的局部线性化 Runge-Kutta 方法
数值分析
2013-12-24 v2 动力系统
摘要
本文研究了 Dormand 和 Prince 的嵌入 Runge-Kutta 公式在初值问题中产生的局部线性化效应。为此，定义了嵌入局部线性化 Runge-Kutta 公式，并通过详尽的数值模拟分析了其性能。对于具有不同动力学特性的各种著名物理方程，模拟结果表明，局部线性化公式表现出比原始公式显著更高的精度，这意味着时间步长数量的大幅减少，从而敏感地降低了其自适应实现的整体计算成本。
引用
@article{arxiv.1209.1415,
title = {Locally Linearized Runge Kutta method of Dormand and Prince},
author = {Juan Carlos Jimenez and Alina Sotolongo and Jose Miguel Sanchez-Bornot},
journal= {arXiv preprint arXiv:1209.1415},
year = {2013}
}
备注
In this version, the local truncation errors of the Locally Linearized Runge Kutta formulas are included and the results of new simulations with crude and refined tolerances are added. Tables are now better organized and displayed in more compact way. Additional information about the High Order Local Linearization method was added as well. Research Memo. No.1152, 02/21/2012, The Institute of Statistical Mathematics, Tokyo