A Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations

S. A. M.Yatim; Z. B.Ibrahim; K. I.Othman; M. B.Suleiman

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A Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations

机译：求解刚性常微分方程的数值方法的定量比较。

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We derive a variable step of the implicit block methods based on the backward differentiation formulae (BDF) for solving stiff initial value problems (IVPs). A simplified strategy in controlling the step size is proposed with the aim of optimizing the performance in terms of precision and computation time. The numerical results obtained support the enhancement of the method proposed as compared to MATLAB's suite of ordinary differential equations (ODEs) solvers, namely, ode15s and ode23s.

机译：我们基于后向微分公式（BDF）导出了隐式块方法的可变步骤，以解决刚性初值问题（IVP）。提出了一种控制步长的简化策略，目的是在精度和计算时间方面优化性能。与MATLAB的一组常微分方程（ODE）求解器（即ode15和ode23）相比，所获得的数值结果支持所提出方法的增强。

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《Mathematical Problems in Engineering: Theory, Methods and Applications》 |2011年第3期|共12页
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S. A. M.Yatim; Z. B.Ibrahim; K. I.Othman; M. B.Suleiman;
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1. A Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations [J] . S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, Mathematical Problems in Engineering . 2011,第PTa3期

机译：求解常微分方程的数值方法的定量比较
2. A Class of Linearly Implicit Numerical Methods for Solving Stiff Ordinary Differential Equations [J] . S.S. Filippov, A.V. Tygliyan The Open Numerical Methods Journal . 2010,第1期

机译：一类求解刚性常微分方程的线性隐数值方法。
3. 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。
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. Asymptotic methods in the numerical solution of stiff ordinary differential equations. [D] . Parris, Ralph. 1989

机译：刚性常微分方程数值解的渐近方法。
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 Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations [O] . S. A. M. Yatim, Z. B. Ibrahim, K. I. Othman, 2011

机译：求解常见差分方程的数值方法的定量比较
8. Use of Block Factorization Iterative Methods in a Stiff ODE (Ordinary Differential Equations) Solver for Two-Dimensional Method-of-Lines Applications [R] . Salane, D. E. 1987

机译：在用于二维线法应用的刚性ODE（常微分方程）求解器中使用块分解迭代方法

A Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations

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