New perturbation-iteration solutions for Bratu-type equations

被引：91

作者：

Aksoy, Yigit ^{[1
]}

Pakdemirli, Mehmet ^{[1
]}

机构：

[1] Celal Bayar Univ, Dept Mech Engn, TR-45140 Muradiye Manisa, Turkey

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 59卷 / 08期

关键词：

Perturbation methods; Perturbation-iteration algorithms; Bratu's equations; DEGREE-OF-FREEDOM; NONLINEAR OSCILLATIONS; PERIODIC-SOLUTIONS; LIMIT-CYCLE; ALGORITHM; SYSTEMS;

D O I：

10.1016/j.camwa.2010.01.050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Perturbation-iteration theory is systematically generated for both linear and nonlinear second-order differential equations and applied to Bratu-type equations. Different perturbation-iteration algorithms depending upon the number of Taylor expansion terms are proposed. Using the iteration formulas derived using different perturbation-iteration algorithms, new solutions of Bratu-type equations are obtained. Solutions constructed using different perturbation-iteration algorithms are contrasted with each other as well as with numerical solutions. It is found that algorithms with more Taylor series expansion terms yield more accurate results. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：2802 / 2808

页数：7

共 31 条

[1]

[Anonymous], 2010, Nonlinear Sci. Lett. A, DOI DOI 10.4236/OALIB.1106601

[2]

Boyd J. P., 1986, Journal of Scientific Computing, V1, P183, DOI 10.1007/BF01061392

[3] Chebyshev polynomial expansions for simultaneous approximation of two branches of a function with application to the one-dimensional Bratu equation [J].

Boyd, JP .

APPLIED MATHEMATICS AND COMPUTATION, 2003, 143 (2-3) :189-200

[4] An algorithm for solving boundary value problems [J].

Deeba, E ;

Khuri, SA ;

Xie, SS .

JOURNAL OF COMPUTATIONAL PHYSICS, 2000, 159 (02) :125-138

[5]

Feng XL, 2008, TOPOL METHOD NONL AN, V31, P243

[6] HE'S ITERATION PERTURBATION METHOD TO NONLINEAR OSCILLATIONS OF MECHANICAL SYSTEMS WITH SINGLE-DEGREE-OF FREEDOM [J].

Ganji, D. D. ;

Karimpour, S. ;

Ganji, S. S. .

INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2009, 23 (11) :2469-2477

[7] Iteration perturbation method for strongly nonlinear oscillations [J].

He, JH .

JOURNAL OF VIBRATION AND CONTROL, 2001, 7 (05) :631-642

[8] Limit cycle and bifurcation of nonlinear problems [J].

He, JH .

CHAOS SOLITONS & FRACTALS, 2005, 26 (03) :827-833

[9] Homotopy perturbation method: a new nonlinear analytical technique [J].

He, JH .

APPLIED MATHEMATICS AND COMPUTATION, 2003, 135 (01) :73-79

[10] Linearized perturbation technique and its applications to strongly nonlinear oscillators [J].

He, JH .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2003, 45 (1-3) :1-8

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