gamal

جمال محمد إسماعيل حسان

استاذ مساعد - استاذ مساعد بقسم الرياضيات - كلية العلوم - جامعة سوهاج

كلية العلوم

العنوان: قسم الرياضيات - كلية العلوم - جامعة سوهاج

7

إعجاب
Analytical Solutions of Strongly Non-linear Problems by the Iteration Perturbation Method
This paper applies modified He's iteration perturbation method to study periodic solutions of strongly nonlinear oscillators. Some examples are given to illustrate the effectiveness and convenience of the method. The results are compared with the numerical solution and the comparison showed a proper accuracy of this method. إقراء المزيد

Solution of a Quadratic Non-Linear Oscillator by Elliptic Homotopy Averaging Method
In this paper, the periodic solutions of a strongly quadratic nonlinear oscillator whose motion is described with the generalized Van der Pol equation are studied. A new method based on homotopy and averaging is employed to determine the limit cycle motion. Three types of quadratic nonlinearity are considered: the coefficients of the linear and quadratic terms are positive, the coefficient ... إقراء المزيد

Solutions of Nonlinear Oscillators by Iteration Perturbation Method
In this paper, the iteration perturbation method is applied to solve nonlinear oscillations. Two examples are given to illustrate the effectiveness and convenience of this iteration procedure. Comparison with the numerical solutions is also presented, revealing that this iteration leads to accurate solutions. إقراء المزيد

Application of Homotopy Perturbation Method and Parameter Expanding Method to Fractional Van der Pol Damped Nonlinear Oscillator
In this study, homotopy perturbation method and parameter expanding method are applied to the motion equations of two nonlinear oscillators. Our results show that both the (HPM) and (PEM) yield the same results for the nonlinear problems. In comparison with the exact solution, the results show that these methods are very convenient for solving nonlinear equations and also can be ... إقراء المزيد

Analytical and Approximate Solutions to the Fee Vibration of Strongly Nonlinear Oscillators
In this paper, we implement a new approach coupled with the iteration method. This procedure is obtained by combining He’s frequency-amplitude formulation and He’s energy balance method into a new iteration procedure such that excellent approximate analytical solutions, valid for small as well as large values of amplitude, can be determined for nonlinear oscillators. This study has clarified the motion ... إقراء المزيد

2012 | الكلمات المفتاحية Analytical solutions, strongly nonlinear oscillators,
Periodic solutions of a certain non-linear differential equations
The study of nonlinear oscillators equations is of great importance not only in all areas of physics but also in engineering and other disciplines, since most phenomena in our word are nonlinear and are described by nonlinear equations. Recently, considerable attention has been direct towards the analytical solutions for nonlinear oscillators, for example, elliptic homotopy averaging method, amplitude-frequency formulation, homotopy ... إقراء المزيد

2012 | الكلمات المفتاحية Nonlinear oscillators, He's amplitude-frequency formu, periodic solution,
Applications of He’s Amplitude-Frequency Formulation to the Free Vibration of Strongly Nonlinear Oscillators
In this paper, He's amplitude-frequency formulation is used to obtain a periodic solution of a nonlinear oscillator. We illustrate that He's amplitude-frequency formulation is very effective and convenient and does not require linearization or small perturbation. The obtained results are valid for the whole solution domain with high accuracy. إقراء المزيد

SOLUTIONS OF THE DUFFING-HARMONIC OSCILLATOR BY HE’S ENERGY BALANCE METHOD
ABSTRACT: In this paper, He’s energy balance method is applied to nonlinear oscillators. The obtained results are valid for the whole solution domain with high accuracy. Comparison is made with the solutions obtained by using He’s frequency-amplitude formulation and Runge-Kutta method to show the efficiency of the energy balance method. إقراء المزيد

Periodic solution of the generalized Rayleigh equation
The periodic solutions of a strongly cubic nonlinear oscillator whose motion is described with the generalized Rayleigh equation are studied. Approximate analytic solving methods are introduced. A new method based on homotopy and averaging is developed to determine the limit cycle motion. The obtained analytical solutions are compared with those calculated by the elliptic harmonic balance method with generalized Fourier ... إقراء المزيد