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Using Interval Methods for the Numerical Solution of ODE'S (Ordinary Differential Equations)

机译：使用区间方法求解ODE'（常微分方程）的数值解

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This is a survey article which deals with the advantages of using interval methods for the numerical solution of initial value problems for ordinary differential equations. (Author)

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Nickel, K. L. E.;
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年度 1983
页码 p.1-34
总页数 34
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Numerical methods and procedures; Differential equations; Boundary value problems; Intervals; Computations; Solutions(General); Transformations(Mathematics); Finite difference theory; Iterations; Power series;

机译：数值方法和程序;微分方程;边值问题;区间;计算;解（通用）;变换（数学）;有限差分理论;迭代;幂级数;

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1. In this paper, we implement the fractional complex transform method to convert the nonlinear fractional Klein-Gordon equation (FKGE) to an ordinary differential equation. We use the variational iteration method (VIM) to solve the resulting ODE. The fractional derivatives are presented in terms of the Caputo sense. Some numerical examples are presented to validate the proposed techniques. Finally, a comparison with the numerical solution using Runge-Kutta of order four is given. [J] . M. M. Khader, M. Adel Nonlinear engineering: Modeling and application . 2016,第3期

机译：在本文中，我们采用分数阶复杂变换方法将非线性分数阶Klein-Gordon方程（FKGE）转换为常微分方程。我们使用变分迭代方法（VIM）来解决所得的ODE。分数导数以Caputo形式表示。提出了一些数值例子来验证所提出的技术。最后，与使用四阶Runge-Kutta的数值解进行了比较。
2. Analysis and Comparative Study of Numerical Solutions of Initial Value Problems (IVP) in Ordinary Differential Equations (ODE) With Euler and Runge Kutta Methods [J] . Anthony Anya Okeke, Pius Tumba, Onyinyechi Favour. Anorue, American Journal of Engineering Research . 2019,第8期

机译：普通微分方程（IVP）与欧拉和径格kutta方法的分析与对比研究
3. A Comparative Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with Euler and Runge Kutta Methods [J] . Md. Amirul Islam American Journal of Computational Mathematics . 2015,第3期

机译：欧拉和朗格·库塔方法对常微分方程（ODE）初值问题（IVP）数值解的比较研究
4. The numerical solutions for stiff ordinary differential equations by using interpolated variational iteration method with comparison to exact solutions [C] . Cihan Ciftci, Hatice Sinem Sas Cayci, Mehmet Tarik Atay, International Conference of Numerical Analysis and Applied Mathematics . 2018

机译：与精确解决方案相比，使用内插改性方法使用插值变分迭代方法来实现常规差分方程的数值解
5. High-order Multistep Asynchronous Splitting Methods (MASM) for the numerical solution of multiple-time-scale ordinary differential equations. [D] . Gudla, Pradeep Kumar. 2016

机译：多时间尺度常微分方程数值解的高阶多步异步分裂方法（MASM）。
6. Numerical Discretization-Based Estimation Methods for Ordinary Differential Equation Models via Penalized Spline Smoothing with Applications in Biomedical Research [O] . Hulin Wu, Hongqi Xue, Arun Kumar -1

机译：普通微分方程模型的数值离散化估计方法通过生物医学研究中的应用与惩罚样条平滑平滑
7. A Comparative Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with Euler and Runge Kutta Methods [O] . Md. Amirul Islam 2015

机译：普通微分方程（ODE）初始值问题（IVP）数值解的比较研究与欧拉和跳闸kutta方法
8. Using Interval Methods for the Numerical Solution of ODE'S (Ordinary Differential Equations). [R] . Nickel, K. L. E. 1983

机译：用区间方法求解ODE'（常微分方程）的数值解。

Using Interval Methods for the Numerical Solution of ODE'S (Ordinary Differential Equations)

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