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GHM method for obtaining rationalsolutions of nonlinear differential equations

机译：GHM方法获得非线性微分方程的有理解

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摘要

In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions.>AMS subject classification 34L30

机译：在本文中，我们建议应用通用同伦方法（GHM）来获得非线性微分方程的有理解。它使用一些线性代数项提供了非线性微分方程的高精度表示。为了评估该建议的好处，解决了三个非线性问题，并将其与其他半解析方法或数值方法进行了比较。获得的结果表明，GHM是强大的工具，能够生成高度精确的有理解。> AMS主题分类 34L30

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期刊名称 SpringerPlus
作者
Hector Vazquez-Leal; Arturo Sarmiento-Reyes;
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作者单位

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年(卷),期 -1(4),-1
年度 -1
页码 241
总页数 11
原文格式 PDF
正文语种
中图分类
关键词
General homotopy method Nonlinear differential equations Epidemic model Heat radiation Boundary value;

机译：一般同伦方法;非线性微分方程;流行病模型;热辐射;边值;

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1. Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: further development of the methodology with applications [J] . Vitanov Nikolay K., Dimitrova Zlatinka I., Vitanov Kaloyan N. Applied mathematics and computation . 2015,第Null期

机译：用于获得非线性偏微分方程精确解析解的最简单方程的改进方法：方法的进一步发展与应用
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机译：用于获得非线性偏微分方程精确解析解的最简单方程的改进方法：方法的进一步发展与应用
3. Mixed function method for obtaining exact solution of nonlinear differential-difference equations and coupled NDDEs [J] . Rui WG, Zhu ZN Applied mathematics and computation . 2010,第5期

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4. THE SPATIAL AND TEMPORAL HARMONIC BALANCE METHOD FOR OBTAINING PERIODIC RESPONSES OF A NONLINEAR PARTIAL DIFFERENTIAL EQUATION WITH A LINEAR COMPLEX BOUNDARY CONDITION [C] . Xuefeng Wang, Weidong Zhu Proceedings of the ASME international design engineering technical conferences and computers and information in engineering conference 2017 . 2017

机译：具有线性复杂边界条件的非线性偏微分方程周期响应的时空谐波平衡方法
5. Parallel domain decomposition methods for stochastic partial differential equations and analysis of nonlinear integral equations. [D] . Jin, Chao. 2007

机译：随机偏微分方程的并行域分解方法和非线性积分方程的分析。
6. A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations [O] . Brahim Benhammouda, Hector Vazquez-Leal -1

机译：微分变换方法的一种新的多步技术用于求解某些非线性可变时滞微分方程的解析解
7. GHM method for obtaining rationalsolutions of nonlinear differential equations [O] . 2015

机译：GHM方法获得非线性微分方程的有理解
8. Some Efficient Methods for Obtaining Infinite Series Solutions of n-TH Order Linear Ordinary Differential Equations [R] . Allen, G. 1972

机译：n - TH阶线性常微分方程无穷级数解的一些有效方法

GHM method for obtaining rationalsolutions of nonlinear differential equations

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