Homotopy Methods and Global Convergence

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Thus, the HAM provides the mathematician freedom to choose the equation-type of the high-order deformation equation and the base functions of its solution. Thus, the convergence-control parameter c 0 is a simple way to guarantee the convergence of the homotopy series solution and differentiates the HAM from other analytic approximation methods. The method overall gives a useful generalization of the concept of homotopy. The HAM is an analytic approximation method designed for the computer era with the goal of "computing with functions instead of numbers.


  1. OhioLINK ETD: Jain, Divyanshu;
  2. Homotopy Methods and Global Convergence.
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Inspired by the recent successful applications of the HAM in different fields, a Mathematica package based on the HAM, called BVPh, has been made available online for solving nonlinear boundary-value problems [4]. BVPh is a solver package for highly nonlinear ODEs with singularities, multiple solutions, and multipoint boundary conditions in either a finite or an infinite interval, and includes support for certain types of nonlinear PDEs.

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The HAM has recently been reported to be useful for obtaining analytical solutions for nonlinear frequency response equations. Such solutions are able to capture various nonlinear behaviors such as hardening-type, softening-type or mixed behaviors of the oscillator,. From Wikipedia, the free encyclopedia. Solving Frontier problems of Physics: The decomposition method.

9. Homotopy and Bifurcation

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Homotopy analysis method

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Taiwanese Journal of Mathematics

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Yi Xu , Wenyu Sun. Besides, if the initial point is expanded to Rn, the global convergence of the homotopy method is ensured under a similar condition.

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The numerical results are reported and illustrate that the method is efficient for some nonlinear complementarity problems. More about this item Keywords Nonlinear complementarity problem ; smoothing homotopy method ; smoothing function ; global convergence ; Statistics Access and download statistics. Corrections All material on this site has been provided by the respective publishers and authors.

Louis Fed. Help us Corrections Found an error or omission? RePEc uses bibliographic data supplied by the respective publishers.

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