Three analytic algorithms based on Adomian decomposition, homotopy perturbation and homotopy analysis methods are proposed to solve some models of nonlinear age-structured population dynamics and epidemiology. Truncating the resulting convergent infinite series, we obtain numerical solutions of high accuracy for these models. Three numerical examples are given to illustrate the simplicity and a...

In this paper, an algorithm based on the collocation and homotopy analysis methods, for solving initial-boundary value problems, is introduced. The application of this algorithm is based on the approximation and interpolation of the dependent variables by using suitable functions or polynomials according to their values in the collocation points corresponding to a suitable discretization of the...

In the course of this paper, the Optimal Homotopy Asymptotic Method (OHAM) introduced by Marica is applied to solve linear and nonlinear boundary value problems both for fourth-order integro-differential equations. The following analysis is accompanied by numerical examples whose results show that the Optimal Homotopy Asymptotic Method is highly accurate, convenient and relatively efficient for...

We propose a notion of groupoid homotopy for generalized maps. This notion of groupoid homotopy generalizes the notions of natural transformation and strict homotopy for functors. The groupoid homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As an application we consider orbifolds as groupoids and study the orbifold homotopy between orbifold maps induced by the...

In this paper, Elzaki Homotopy Perturbation Method is employed for solving linear and nonlinear differential equations with a variable coffecient. This method is a combination of Elzaki transform and Homotopy Perturbation Method. The aim of using Elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as Homotopy Perturbat...

the inverse problem of identifying an unknown source control param- eter in a semilinear parabolic equation under an integral overdetermina- tion condition is considered. the series pattern solution of the proposed problem is obtained by using the weighted homotopy analysis method (wham). a description of the method for solving the problem and nding the unknown parameter is derived. finally, tw...

The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to such a classifying space. This gives results on the homotopy classification of maps from a CW -complex to the classifying space of a crossed module and also, ...

We describe, very briefly, the basic ideas and current developments of the homotopy analysis method, an analytic approach to get convergent series solutions of strongly nonlinear problems, which recently attracts interests of more and more researchers. Definitions of some new concepts such as the homotopy-derivative, the convergence-control parameter and so on, are given to redescribe the metho...

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for s...