homotopy


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Related to homotopy: Homotopy groups, Homotopy theory

homotopy

[hō′mäd·ə·pē]
(mathematics)
Between two mappings of the same topological spaces, a continuous function representing how, in a step-by-step fashion, the image of one mapping can be continuously deformed onto the image of the other.
References in periodicals archive ?
In this work we have demonstrated efficiency of the Homotopy analysis transform method (Hatm) and Residual power series method (RPSM) for finding series solutions of linear and nonlinear Schrodinger equations.
We construct the homotopy of the transformed equations as follows
Second, the approximate solutions obtained from the first step are used as initial points in the numerical extension method (homotopy method) for further computation of multiple solutions associated with the EEM system in a larger subspace.
Let us construct the homotopy perturbation equations
The development of analytical solutions through some approximate analytical methods such as the Adomian decomposition method, homotopy analysis method, variation iteration method, and differential transformation method for the flow process has been semianalytic in procedures and applications.
In this part we illustrate the concept of homotopy method.
of the stable homotopy group of the homotopy fixed-point set of f/p.
In [20], we applied appropriate perturbations to the constraint functions and developed a new homotopy method to expand the scope of initial point selection, but involving the inequality constraint cases only.
In this article, we present a detailed analysis of squeezing flow of Newtonian fluids using an improved alteration of the Homotopy Perturbation Method with Laplace Transform.
In the past years, different kind of vigorous techniques has been introduced to find an approximate solution of such type of fractional model of differential equations, such as generalized differential transform method [11], Adomian decomposition method [12], homotopy analysis method [13], homotopy analysis transform method [14], modified Laplace transform method [15], and homotopy perturbation transform method (HPTM) [16-18].
Xu and Liao [4] studied the boundary layer flow over a flat plate with a constant velocity opposite in direction to that of the uniform free stream by using the homotopy analysis method (HAM).