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A Comparison of Explicit Semi-Analytical Numerical Integration Methods for Solving Stiff ODE Systems

机译：求解刚性ODE系统的显式半解析数值积分方法的比较

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摘要

In this study, a comparison among three semi-analytical numerical integration algorithms for solving stiff ODE systems is presented. The algorithms are based on Differential Transform Method (DTM) which are Multiple-Step DTM (MsDTM), Enhanced MsDTM (E-MsDTM) and MsDTM with Pade approximants (MsDTM-P). These methods can be classified as explicit one step semi-analytical numerical integration methods. The error and stability analysis of each method is presented. New important relationships among the methods are introduced. To demonstrate our results, a comparison of the accuracy, stability and computational efficiency of the methods is presented through solving some linear and nonlinear problems arising in applied science and engineering.
机译：在这项研究中，提出了解决刚性ODE系统的三种半解析数值积分算法的比较。该算法基于差分变换方法（DTM），它们是多步DTM（MsDTM），增强型MsDTM（E-MsDTM）和带有Pade近似值的MsDTM（MsDTM-P）。这些方法可以分类为明确的一步半分析数值积分方法。给出了每种方法的误差和稳定性分析。介绍了这些方法之间的新的重要关系。为了证明我们的结果，通过解决应用科学和工程学中出现的一些线性和非线性问题，比较了这些方法的准确性，稳定性和计算效率。

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  • 来源
    《American journal of applied sciences》 |2015年第5期|304-320|共17页
  • 作者

    E.R. El-Zahar; H.M. Habib; M.M. Rashidi; I.M. El-Desoky;

  • 作者单位

    Department of Mathematics, Sciences and Humanities College, Salman Bin Abdulaziz University, Alkharj, 11942, KSA,Department of Basic Engineering Scienc, Engineering Faculty, Shebin El-Kom, Menofia University, Egypt;

    Department of Mathematics, Sciences and Humanities College, Salman Bin Abdulaziz University, Alkharj, 11942, KSA,Department of Basic Engineering Scienc, Engineering Faculty, Shebin El-Kom, Menofia University, Egypt;

    Shanghai Automotive Wind Tunnel Center, Tongji University, Jiading, Shanghai 201804, China;

    Department of Basic Engineering Scienc, Engineering Faculty, Shebin El-Kom, Menofia University, Egypt;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Multiple-Step Differential Transform Methods (MsDTM); Enhanced MsDTM; Pade Approximants; Stiff Problems; Accuracy; Stability;

    机译：多步差分变换方法（MsDTM）;增强型MsDTM;帕德近似值;僵硬的问题;准确性;稳定性;

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