一种基于量子化状态系统的刚性ODE求解方法

doi:10.16182/j.issn1004731x.joss.19-0172

系统仿真学报 ›› 2021, Vol. 33 ›› Issue (1): 46-53.doi: 10.16182/j.issn1004731x.joss.19-0172

一种基于量子化状态系统的刚性ODE求解方法

李志华, 江德, 吴晨佳, 樊志华

杭州电子科技大学机械工程学院,浙江杭州 310018

收稿日期:2019-04-23 修回日期:2019-08-09 发布日期:2021-01-18
作者简介:李志华(1966-),男,博士,教授,研究方向为多领域建模与仿真优化、CAD/CAE。E-mail：D98LZH@263.net
基金资助:
国家重点研发计划“智能机器人”专项(2017YFB1301300),浙江省自然科学基金(LY18E050008,LY19E050013)

A Quantization-based Integration Method for Stiff Ordinary Differential Equations

Li Zhihua, Jiang De, Wu Chenjia, Fan Zhihua

School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, China

Received:2019-04-23 Revised:2019-08-09 Published:2021-01-18

摘要/Abstract

摘要： 量子化状态系统(Quantized State System,QSS)在求解一般常微分方程(Ordinary Differential Equation,ODE)系统时,比传统基于时间离散的积分方法更具优势,但QSS方法不适合求解刚性ODE系统,为此提出一种基于量子化状态系统的步进校正优化算法(Step-correction Optimization Algorithm Based on QSS,SCOA based-on QSS),它结合QSS方法及隐式算法中梯形积分法的思想,以有效提高刚性ODE系统的求解精度和效率。通过对3个典型刚性ODE算例的仿真求解,结果表明,SCOA based-on QSS算法总体上比其他算法更具优势,同时在适当减小量子大小时能显著提高仿真精度。

关键词: 常微分方程, 刚性系统, 量子化状态系统, 数值积分, 仿真

Abstract: QSS(Quantized State System) has advantages over the traditional time-discrete integration methods in solving general ordinary differential equation (ODE) systems, but it is not suitable for solving the stiff ODE systems. To effectively solve the stiff ODE systems, a step-correction optimization algorithm based on QSS (SCOA based-on QSS) is proposed, which combines the ideas of the QSS method and the implicit trapezoidal integral method. The simulation results of three typical stiff ODE cases show that the SCOA based-on QSS algorithm has advantages over other algorithms, and the simulation accuracy can be significantly improved by appropriately reducing the quantum size.

Key words: ordinary differential equation, stiff system, quantized state system, numerical integration, simulation

中图分类号:

TP391

李志华, 江德, 吴晨佳, 樊志华. 一种基于量子化状态系统的刚性ODE求解方法[J]. 系统仿真学报, 2021, 33(1): 46-53.

Li Zhihua, Jiang De, Wu Chenjia, Fan Zhihua. A Quantization-based Integration Method for Stiff Ordinary Differential Equations[J]. Journal of System Simulation, 2021, 33(1): 46-53.

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一种基于量子化状态系统的刚性ODE求解方法

A Quantization-based Integration Method for Stiff Ordinary Differential Equations

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