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帕德近似法在求解非线性微分方程中的直接应用。

Direct application of Padé approximant for solving nonlinear differential equations.

作者信息

Vazquez-Leal Hector, Benhammouda Brahim, Filobello-Nino Uriel, Sarmiento-Reyes Arturo, Jimenez-Fernandez Victor Manuel, Garcia-Gervacio Jose Luis, Huerta-Chua Jesus, Morales-Mendoza Luis Javier, Gonzalez-Lee Mario

机构信息

Electronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, Mexico.

Higher Colleges of Technology, Abu Dhabi Men's College, P.O. Box 25035, Abu Dhabi, United Arab Emirates.

出版信息

Springerplus. 2014 Sep 27;3:563. doi: 10.1186/2193-1801-3-563. eCollection 2014.

DOI:10.1186/2193-1801-3-563
PMID:25332863
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC4194307/
Abstract

UNLABELLED

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant.

AMS SUBJECT CLASSIFICATION

34L30.

摘要

未标注

本文提出了一种直接应用帕德方法来求解非线性微分方程近似解的程序。此外，我们给出了一些案例研究，展示了该方法相较于其他半解析方法在生成高精度有理近似解方面的优势。所测试的非线性方程类型包括：一个高度非线性边值问题、一个微分代数振子问题以及一个渐近问题。通过直接应用帕德方法获得的高精度便捷近似解表明，该方案在近似各种问题方面具有很高的潜力。更重要的是，直接应用帕德近似有助于避免先前使用诸如泰勒级数法、同伦摄动法、阿多米安分解法、同伦分析法、变分迭代法等近似方法作为工具来获得幂级数解，以便后续用帕德近似进行处理。

美国数学学会主题分类

34L30 。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9c9f/4194307/686647c90238/40064_2014_1281_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9c9f/4194307/26a2699818af/40064_2014_1281_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9c9f/4194307/686647c90238/40064_2014_1281_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9c9f/4194307/26a2699818af/40064_2014_1281_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/9c9f/4194307/686647c90238/40064_2014_1281_Fig2_HTML.jpg

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本文引用的文献

1
Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.用于求解在有限区间上定义的具有混合边界条件的非线性微分方程的修正泰勒级数方法。
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由于部分滑移导致的具有拉伸边界的流动的近似解。
Int Sch Res Notices. 2014 Nov 24;2014:747098. doi: 10.1155/2014/747098. eCollection 2014.