Numerical comparison of methods for solving second-order ordinary initial value problems

Kamel Al-Khaled; M. Naim Anwar

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Numerical comparison of methods for solving second-order ordinary initial value problems

机译：二阶普通初值问题求解方法的数值比较

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摘要

In this paper, we apply Adomian decomposition method (shortly, ADM) to develop a fast and accurate algorithm of a special second-order ordinary initial value problems. The ADM does not require discretization and consequently of massive computations. This paper is particularly concerned with the ADM and the results obtained are compared with previously known results using the Quintic C~2-spline integration methods. The numerical results demonstrate that the ADM is relatively accurate and easily implemented.

机译：在本文中，我们使用Adomian分解方法（简称ADM）来开发一种快速，准确的特殊二阶普通初值问题的算法。 ADM不需要离散化，因此不需要大量计算。本文特别关注ADM，并使用Quintic C〜2样条积分方法将获得的结果与先前已知的结果进行比较。数值结果表明，ADM相对准确且易于实施。

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来源
《Applied Mathematical Modelling》 |2007年第2期|p.292-301|共10页
作者
Kamel Al-Khaled; M. Naim Anwar;
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作者单位

Department of Mathematics, Jordan University of Science and Technology, IRBID 22110, Jordan;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
quintic spline; adomian decomposition method; approximate solutions; second-order initial value problem;

机译：五次样条;Adomian分解法;近似解;二阶初值问题;

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1. Quintic C~2-spline integration methods for solving second-order ordinary initial value problems [J] . S. Sallam, M. Naim Anwar Journal of Computational and Applied Mathematics . 2000,第1a2期

机译：用于解决二阶普通初值问题的Quintic C〜2样条积分方法
2. A new method for solving singular initial value problems in the second-order ordinary differential equations [J] . Wazwaz AM. Applied mathematics and computation . 2002,第1期

机译：解决二阶常微分方程奇异初值问题的新方法
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. Comparison of several difference methods of solving second-order ordinary differential equation [C] . Yanfeng Liu, Le Cao, Qian Yang, Symposia on Electromagnetic and Electronic Engineering . 2015

机译：求解二阶常微分方程几种差分方法的比较
5. Topics in numerical relativity: Solving the initial value problem using adaptive mesh refinement, examining evolution stability using spectral methods, and finding apparent horizons using a mean curvature-level set method [D] . Lowe, Lisa L. 2008

机译：数值相对论的主题：使用自适应网格细化解决初值问题，使用频谱方法检查演化稳定性，并使用平均曲率级集方法找到视在地平线
6. Role of lean leadership in the lean maturity—second-order problem-solving relationship: a mixed methods study [O] . Arie Bijl, Kees Ahaus, Gwenny Ruël, 2019

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7. Quintic C2-spline integration methods for solving second-order ordinary initial value problems [O] . Sallam S., Anwar M.Naim 2000

机译：用于解决二阶普通初值问题的Quintic C2-样条积分方法

Numerical comparison of methods for solving second-order ordinary initial value problems

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