We investigate the hard nonresonant excitation of the forced Duffing equation with a positive damping parameter E. Using the symbolic manipulation system MACSYMA, a computer algebra system. we derive the two term perturbation expansion by the method of multiple time scales. The resulting approximate solution is valid for small values of the coefficient e As the damping parameter e increases, th...

A continuum model of globular proteins proposed by Talanquer and Oxtoby [J. Chem. Phys. 109, 223 (1998)] is investigated numerically, with particular emphasis on the region near the metastable fluid-fluid coexistence curve. Classical nucleation theory is shown to be invalid not only in the vicinity of the metastable critical point but also close to the liquidus line. An approximate analytic sol...

In this paper, the perturbation method and Padé transformation are used to provide an approximate solution of elliptic integrals of the second kind and of complete integrals of the first kind. Besides, we used the obtained results to calculate an analytic expression for the period of a simple pendulum. The method has an acceptable accuracy for high values of the initial amplitude, compared to t...

We show that a harmonic oscillator subject to a sudden change of mass produces squeezed states. Our study is based on an approximate analytic solution to the time-dependent harmonic oscillator equation with a subperiod function parameter. This continuous treatment differs from former studies that involve the matching of two time-independent solutions at the discontinuity. This formalism require...

This paper discusses a numerical method based on Least Squares Support Vector Machines (LS-SVMs) for solving linear time varying initial and boundary value problems in Differential Algebraic Equations (DAEs). The method generates a closed form (model-based) approximate solution. The results of numerical experiments on different systems with index from 0 to 3, are presented and compared with ana...

This paper presents a new approach to machine health monitoring based on the Approximate Entropy (ApEn), which is a statistical measure that quantifies the regularity of a time series, such as vibration signals measured from an electrical motor or a rolling bearing. As the working condition of a machine system deteriorates due to the initiation and/or progression of structural defects, the numb...

In this paper a numerical method for solving second order fuzzy differential equations under generalized differentiability is proposed. This method is based on the interpolating a solution by piecewise polynomial of degree 4 in the range of solution. Moreover we investigate the existence, uniqueness and convergence of approximate solutions. Finally the accuracy of piecewise approximate method b...

In this work, we introduce an analytical approximate black hole solution in Einstein-Cubic gravity. To obtain complete solutions, construct the near horizon and asymptotic solutions as first step. Then, analytic are obtained through continued fraction expansion. We also compute thermodynamic quantities use law Smarr formula to for quantities. Finally, follow same approach new static with differ...

Baryogenesis by heavy-neutrino decay and sphaleron reprocessing of both baryon and lepton number is reconsidered, paying special attention to the flavour structure of the general evolution equations and developing an approximate but sufficiently accurate analytic solution to the prototype evolution equation. Two different models of neutrino masses are examined, based on an Abelian U(1) or a non...

In this paper, a method for finding an approximate solution of a class of two-dimensional nonlinear Volterra integral equations of the first-kind is proposed. This problem is transformedto a nonlinear two-dimensional Volterra integral equation of the second-kind. The properties ofthe bivariate shifted Legendre functions are presented. The operational matrices of integrationtogether with the produ...