A Comparison of Explicit Semi-Analytical Numerical Integration Methods for Solving Stiff ODE Systems
A Comparison of Explicit Semi-Analytical Numerical Integration Methods for Solving Stiff ODE Systems
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DOI：
10.3844/ajassp.2015.304.320
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发表时间：
2015-06
期刊：
影响因子：
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通讯作者：
E. El-Zahar;H. Habib;Mohammad Mehdi Rashidi;I. M. El-Desoky
中科院分区：
文献类型：
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作者：
E. El-Zahar;H. Habib;Mohammad Mehdi Rashidi;I. M. El-Desoky
在本研究中，对求解刚性 ODE 系统的三种半解析数值积分算法进行了比较。这些算法基于微分变换方法 (DTM)，包括多步 DTM (MsDTM)、增强型 MsDTM (E-MsDTM) 和具有 PadA© 近似值的 MsDTM (MsDTM-P)。这些方法可以归类为显式一步半解析数值积分方法。给出了每种方法的误差和稳定性分析。引入了方法之间新的重要关系。为了证明我们的结果，通过解决应用科学和工程中出现的一些线性和非线性问题，对这些方法的准确性、稳定性和计算效率进行了比较。
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 PadA© 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.