although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.here, after criticizi...

Coupled atomistic–continuum methods can describe large domains and model dynamic material behavior for a much lower computational cost than traditional atomistic techniques. However, these multiscale frameworks suffer from wave reflections at the interfaces due to numerical discrepancy between fine-scaled coarse-scaled models. Such are non-physical may lead unfavorable outcomes such as artifici...

Abstract The aim of this work is the numerical homogenization a parabolic problem with several time and spatial scales using heterogeneous multiscale method. We replace actual cell an alternate one, Dirichlet boundary initial values instead periodic conditions. Further, we give detailed priori error analysis fully discretized, i.e., in space for both macroscopic problem, Numerical experiments i...

objective: the aim of this study is to evaluate the effectiveness of the metacognitive model in treating post-traumatic stress disorder. method: in a single-subject experimental trial of multiple baseline type, the treatment process was carried out on an 18-year-old male subject. the patient satisfied the dsm-iv criteria for ptsd and was assessed for pre-duration and post treatment. the scales ...

In this paper we examine fluctuation and frequency of the governing equation ofoscillator with odd and even nonlinearities without damping and we present a new efficientmodification of the He’s homotopy perturbation method for this equation. We applied standard andmodified homotopy perturbation method and compare them with the numerical solution (NS), also weapplied He’s Energy balance method (...

In this study, the method of multiple scales is used to perform a nonlinear vibration analysis of a mechanical system in two cases; with dry and lubricated clearance joints. In the dry contact case, the Lankarani-Nikravesh model is used to represent the contact force between the joined bodies. The surface elasticity is modeled as a nonlinear spring-damper element. Primary resonance is discussed...