In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

1 .l Summary IN [l] QUILLEN introduced the notion of a model category (a category together with three classes of maps: weak equivalences, fibrations and cofibrations, satisfying certain axioms (1.4 (iv))) as a general framework for “doing homotopy theory”. To each model category M there is associated a homotopy category. If W C M denotes the subcategory of the weak equivalences, then this homot...

in this work, the blasius equation is studied. homotopy perturbation method (hpm) and homotopy analysis method (ham) are applied to obtain its solution. comparison with variational iteration method (vim) is made to highlight the significant features of employed methods and their capability of handling nonlinear problems. the outcome shows the success of (hpm) and (ham) for solving nonlinear pro...

y In this paper we calculate the 2-primary v 1-periodic homotopy groups of the sym-plectic groups Sp(n). The proof utilizes new methods of calculating the unstable Novikov spectral sequence. One corollary is that some homotopy group of Sp(n) contains an element of order 2 2n?1. 1 Main theorem In this paper we calculate the 2-primary v 1-periodic homotopy groups of the sym-plectic groups Sp(n). ...

The Black–Scholes option pricing model is one of the most significant achievements in modern investment science. However, many factors are constantly fluctuating actual financial market pricing, such as risk-free interest rate, stock price, underlying and security price volatility may be inaccurate real world. Therefore, it great practical significance to study fractional fuzzy model. In this p...

Although homotopy-based methods, namely homotopy analysis method and homotopy perturbation method, have largely been used to solve functional equations, there are still serious questions on the convergence issue of these methods. Some authors have tried to prove convergence of these methods, but the researchers in this article indicate that some of those discussions are faulty. Here, after crit...

The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for crossed complexes, using detailed results on the appropriate Eilenberg–Zilber theory, and of its relation to simplicial homotopy coh...

A fundamental construction in the study of stable homotopy is the free infinite loop space generated by a space X. This is the colimit QX = lim −→ ΩΣX. The i homotopy group of QX is canonically isomorphic to the i stable homotopy group of X. Thus, one may obtain stable information about X by obtaining topological results about QX. One such result is the Kahn-Priddy theorem [7]. In another direc...