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Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix.

机译：基于状态转移矩阵的具有时变和非线性系数的常微分方程的数值格式。

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摘要

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

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作者
Bartels, R. E.;
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年度 2002
页码 1-24
总页数 24
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Differential equations; Matrices(Mathematics); Boundary value problems; Accuracy; Coefficients; Nonlinear systems; Polynomials; Time dependence;

机译：微分方程;矩阵（数学）;边值问题;精度;系数;非线性系统;多项式;时间依赖性;

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专利

1. Sieve estimation of constant and time-varying coefficients in nonlinear ordinary differential equation models by considering both numerical error and measurement error [J] . Xue H., Miao H., Wu H. The Annals of Statistics: An Official Journal of the Institute of Mathematical Statistics . 2010,第4期

机译：同时考虑数值误差和测量误差的非线性常微分方程模型的常数和时变系数的筛估计
2. A numerical scheme for the blow-up time of solutions of a system of nonlinear ordinary differential equations [J] . Aroldo Perez, Jose Villa-Morales Applied numerical mathematics . 2022,第Jana期

机译：非线性常微分方程系统解的爆破时间的数值方案
3. Numerical solution of nonlinear inverse coefficient problems for ordinary differential equations [J] . Aida-Zade K.R., Kuliev S.Z. Computational mathematics and mathematical physics . 2011,第5期

机译：常微分方程非线性反系数问题的数值解
4. Numerical Solution for Nonlinear Time-Fractional Partial Differential Equation With Variable Coefficient Using Reproducing Kernel Hibert Space Method [C] . Nourhane Attia, Djamila Seba, Abdelkader Nour International Conference on Mathematics and Information Technology . 2020

机译：非线性核函数希尔伯特空间方法求解非线性时变分数阶偏微分方程
5. THE APPLICATION OF NONLINEAR PROGRAMMING TO THE OPTIMIZATION OF MULTISTEP METHODS FOR THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS. [D] . HANEY, RICHARD FRANCIS. 1980

机译：非线性编程在优化多步法求解常微分方程数值解中的应用。
6. Sieve Estimation of Constant and Time-Varying Coefficients in Nonlinear Ordinary Differential Equation Models by Considering Both Numerical Error and Measurement Error [O] . Hongqi Xue, Hongyu Miao, Hulin Wu -1

机译：恒的筛估计和时变系数的非线性常微分方程模型同时考虑数值误差和测量误差
7. Sieve estimation of constant and time-varying coefficients in nonlinear ordinary differential equation models by considering both numerical error and measurement error [O] . Hongqi Xue, Hongyu Miao, Hulin Wu 2016

机译：通过考虑数值误差和测量误差，对非线性常微分方程模型中常数和时变系数的sieve估计
8. A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix [R] . Bartels, Robert E. 2002

机译：基于状态转移矩阵的具有时变和非线性系数的常微分方程的数值格式

Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix.

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