duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...

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 (...

This paper applies He’s Energy balance method (EBM) to study periodic solutions of strongly nonlinear systems such as nonlinear vibrations and oscillations. The method is applied to two nonlinear differential equations. Some examples are given to illustrate the effectiveness and convenience of the method. The results are compared with exact solutions which lead us showing a good accuracy. The m...

Energy balance method EBM is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the firstand second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreemen...

Energy Balance Models (EBM) are conceptual models which have proved useful in the study of planetary climate. The focus of EBM is placed on large scale climate components such as incoming solar radiation, albedo, outgoing longwave radiation and heat transport, and their interactions. Until recently, their study has centered on equilibrium solutions of an associated model equation, with no consi...

Several extensions of energy balance models (EBMs) are explored in which (i) sea ice acts to insulate the atmosphere from the ocean and (ii) ocean heat transport is allowed to have some meridional structure controlled by the wind, with minima at which the ice edge can rest. These new models support multiple stable ice edges not found in the classical EBM and a hysteresis loop capable of generat...

The major criticisms and limitations of Evidence-Based Medicine (EBM) appearing in the literature over the past decade can be summarized and categorized into five recurring themes. The themes include: reliance on empiricism, narrow definition of evidence, lack of evidence of efficacy, limited usefulness for individual patients, and threats to the autonomy of the doctor/patient relationship. Ana...

We examine the variability of the ocean’s thermohaline circulation in a Oceanic General Circulation Model (OGCM) coupled to a two dimensional atmospheric Energy Balance Model (EBM). The EBM calculates air temperatures by balancing heat fluxes, including that from the ocean surface; air temperature and ocean circulation evolve together without imposed temperature restrictions except specificatio...