Considering qualitative behavior of a non-linear dynamical system often leads to first simplifying the differential equations or finding their normal forms. A perturbation technique for computing normal forms is presented. This technique, associated with the method of multiple scales, can be used to systematically find a unique form for a given set of differential equations. The technique is di...

Perturbation techniques are frequently used in the study of nonlinear dynamical systems, in particular, for bifurcation and stability analyses. In this paper, four most popular perturbation methods – Lindstedt-Poincaré (LP) approach, timeaveraging (TA), multiple time scales (MTS) and the intrinsic harmonic balancing (IHB) – are particularly considered to compare their accuracy of the bifurcatio...

in this paper, we conduct a comparative study between the homotopy perturbation method (hpm) and adomian’s decomposition method (adm) for analytic treatment of nonlinear volterra integral equations, and we show that the hpm with a specific convex homotopy is equivalent to the adm for these type of equations.

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...

We present a method for constructing gauge-invariant cosmological perturbations which are gaugeinvariant up to second order. As an example we give the gauge-invariant definition of the second order curvature perturbation on uniform density hypersurfaces. Using only the energy conservation equation we show that this curvature perturbation is conserved at second order on large scales for adiabati...