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.

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  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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On a natural homotopy between linear and nonlinear single-layer networks.

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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.

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