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Modified HPMs Inspired by Homotopy Continuation Methods

机译：受同伦连续方法启发的改良HPM

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摘要

Nonlinear differential equations have applications in the modelling area for a broad variety of phenomena and physical processes; having applications for all areas in science and engineering. At the present time, the homotopy perturbation method (HPM) is amply used to solve in an approximate or exact manner such nonlinear differential equations. This method has found wide acceptance for its versatility and ease of use. The origin of the HPM is found in the coupling of homotopy methods with perturbation methods. Homotopy methods are a well established research area with applications, in particular, an applied branch of such methods are the homotopy continuation methods, which are employed on the numerical solution of nonlinear algebraic equation systems. Therefore, this paper presents two modified versions of standard HPM method inspired in homotopy continuation methods. Both modified HPMs deal with nonlinearities distribution of the nonlinear differential equation. Besides, we will use a calcium-induced calcium released mechanism model as study case to test the proposed techniques. Finally, results will be discussed and possible research lines will be proposed using this work as a starting point.
机译：非线性微分方程在建模领域具有广泛的现象和物理过程应用。在科学和工程的所有领域都有应用。目前，同伦摄动法（HPM）已被广泛用于近似或精确地求解此类非线性微分方程。该方法的多功能性和易用性已被广泛接受。 HPM的起源是同伦方法与摄动方法的结合。同伦方法是一个有广泛应用前景的研究领域，特别是此类方法的一个应用分支是同伦连续方法，该方法被用于非线性代数方程组的数值解。因此，本文介绍了受同态延续方法启发的标准HPM方法的两个修改版本。两种改进的HPM都处理非线性微分方程的非线性分布。此外，我们将使用钙诱导的钙释放机制模型作为研究案例来测试所提出的技术。最后，将讨论结果并以这项工作为起点来提出可能的研究方向。

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  • 来源
    《Mathematical Problems in Engineering》 |2012年第4期|p.309123.1-309123.19|共19页
  • 作者

    Hector Vazquez-Leal; Uriel Filobello-Nino; Roberto Castaneda-Sheissa; Luis Hernandez-Martinez; Arturo Sarmiento-Reyes;

  • 作者单位

    Electronic Instrumentation and Atmospheric Sciences School, University of Veracruz, Circuito Gonzalo Aguirre Beltran s, 91000 Xalapa, VER, Mexico;

    Electronic Instrumentation and Atmospheric Sciences School, University of Veracruz, Circuito Gonzalo Aguirre Beltran s, 91000 Xalapa, VER, Mexico;

    Electronic Instrumentation and Atmospheric Sciences School, University of Veracruz, Circuito Gonzalo Aguirre Beltran s, 91000 Xalapa, VER, Mexico;

    Department of Electronics, National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro 1, 72840 Sta. Maria Tonantzintla, PUE, Mexico;

    Department of Electronics, National Institute for Astrophysics, Optics and Electronics, Luis Enrique Erro 1, 72840 Sta. Maria Tonantzintla, PUE, Mexico;

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