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

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

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

机译：刚性ODE系统的显式半解析数值积分方法比较科学出版物

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> >In this study, a comparison among three semi-analyticalnumerical integration algorithms for solving stiff ODE systems is presented.The algorithms are based on Differential Transform Method (DTM) which areMultiple-Step DTM (MsDTM), Enhanced MsDTM (E-MsDTM) and MsDTM with Padéapproximants (MsDTM-P). These methods can be classified as explicit one stepsemi-analytical numerical integration methods. The error and stability analysisof each method is presented. New important relationships among the methods areintroduced. To demonstrate our results, a comparison of the accuracy, stabilityand computational efficiency of the methods is presented through solving somelinear and nonlinear problems arising in applied science and engineering.

机译： > >在本研究中，对解决刚性ODE系统的三种半解析数字积分算法进行了比较。这些算法基于差分变换法（DTM），即多步DTM（MsDTM），增强型MsDTM（E-MsDTM）和具有Padéapproximants的MsDTM（MsDTM-P）。这些方法可以分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。介绍了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，比较了该方法的准确性，稳定性和计算效率。

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《American journal of applied sciences》 |2015年第5期|共页
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E.R. El-Zahar; H.M. Habib; I.M. El-Desoky; M.M. Rashidi;
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1. A Comparison of Explicit Semi-Analytical Numerical Integration Methods for Solving Stiff ODE Systems [J] . E.R. El-Zahar, H.M. Habib, M.M. Rashidi, American journal of applied sciences . 2015,第5期

机译：求解刚性ODE系统的显式半解析数值积分方法的比较
2. A NON-LINEAR ABSOLUTELY-STABLE EXPLICIT NUMERICAL INTEGRATION ALGORITHM FOR STIFF INITIAL-VALUE PROBLEMS | Science Publications [J] . Essam R. El-Zahar American journal of applied sciences . 2013,第11期

机译：一种非线性绝对稳定的刚性初始值问题的明确数值积分算法科学出版物
3. Explicit Numerical Methods for Solving Stiff Dynamical Systems [J] . Suying Zhang and Jiangdan Li Journal of Computational and Nonlinear Dynamics . 2011,第4期

机译：求解刚性动力系统的显式数值方法
4. SOLVING THE BATEMAN EQUATIONS IN CASMO5 USING IMPLICIT ODE NUMERICAL METHODS FOR STIFF SYSTEMS [C] . Joshua M. Hykes, Rodolfo M. Ferrer International conference on mathematics and computational methods applied to nuclear science and engineering . 2013

机译：用刚度数值方法求解CASMO5中的贝特曼方程。
5. Numerical methods for solving stiff differential equations. [D] . Boden, Craig Travis. 1991

机译：求解刚性微分方程的数值方法。
6. Convergence Analysis and Numerical Study of a Fixed-Point Iterative Method for Solving Systems of Nonlinear Equations [O] . Na Huang, Changfeng Ma -1

机译：求解非线性方程组的不动点迭代法的收敛性分析和数值研究
7. Exploration of FPGA-Based Hardware Designs for QR Decomposition for Solving Stiff ODE Numerical Methods Using the HARP Hybrid Architecture [O] . Carlos Alberto Oliveira de Souza Junior, João Bispo, João M. P. Cardoso, 2020

机译：基于FPGA的硬件设计探讨了QR分解，用于使用HARP混合架构解决硬颂数值
8. Numerical solution of nonlinear algebraic equations in stiff ODE solving (1986--89)---Quasi-Newton updating for large scale nonlinear systems (1989--90). Final report, 1986--1990 [R] . Walker, H. F. 1990

机译：非线性代数方程在刚性ODE求解中的数值解（1986--89）---大规模非线性系统的拟牛顿更新（1989--90）。最终报告，1986- 1990

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

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