The dynamics of cables with concentrated loads is studied using a direct perturbation method (DPM) combined with multiple time scales. A general cable model is assumed to have complex loads, including nonlinear aerodynamic force and concentrated masses. An early developed perturbation method––DPM–– is applied to investigate the cable s motion. This approach does not need to transform the origin...

We consider the dynamics of a multi-component scalar field on super-horizon scales in the context of inflationary cosmology. We present a method to solve the perturbation equations on super-horizon scales, i.e., in the long wavelength limit, by using only the knowledge of spatially homogeneous background solutions. In doing so, we clarify the relation between the perturbation equations in the l...

Perturbation of a steadily propagating crack with a straight edge is solved using the method of matched asymptotic expansions (MAE). This provides a simplified analysis in which the inner and outer solutions are governed by distinct mechanics. The inner solution contains the explicit perturbation and is governed by a quasi-static equation. The outer solution determines the radiation of energy a...

Perturbation of a steadily propagating crack with a straight edge is solved using the method of matched asymptotic expansion (MAE). This provides a simplified analysis in which the inner and outer solutions are governed by distinct mechanics. The inner solution contains the explicit perturbation and is governed by a quasistatic equation. The outer solution determines the radiation of energy awa...

in this article, we demonstrate an analytic-numeric solution for some dynamical systems using the multistagehomotopy perturbation method. the method yields results that are in complete agreement with their numericalcounterparts.

A model of a strip of cardiac tissue consisting of a one-dimensional chain of cardiac units is derived in the form of a non-linear partial difference equation. Perturbation analysis is performed on this equation, and it is shown that regular perturbations are inadequate due to the appearance of secular terms. A singular perturbation procedure known as the method of multiple scales is shown to p...

in this paper, the solution of the evolutionaryfourth-order in space, sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{hpm}). the results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.