Yazar "Madani, M." seçeneğine göre listele

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    Analytical Solutions for Autonomous Conservative Nonlinear Oscillator
    (Walter De Gruyter Gmbh, 2010) Yazdi, Mohammad Kalami; Khan, Yasir; Madani, M.; Askari, H.; Saadatnia, Z.; Yildirim, Ahmet
    This paper adapts the Energy Balance Method (EBM) and Frequency Amplitude Formulation to solve the free vibrations of a conservative oscillator with inertia and static cubic non-linearities. Case studies on the effects of the time response are presented. The results that obtained from the EBM and FAF are then compared with those from the numerical solution in order to verify the accuracy of the proposed method.
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    Application of homotopy perturbation and numerical methods to the circular porous slider
    (Emerald Group Publishing Ltd, 2012) Madani, M.; Khan, Yasir; Mahmodi, Gh.; Faraz, Naeem; Yildirim, Ahmet; Nasernejad, B.
    Purpose - The purpose of this paper is to present the problem of three-dimensional flow of a fluid of constant density forced through the porous bottom of a circular porous slider moving laterally on a flat plate. Design/methodology/approach - The transformed nonlinear ordinary differential equations are solved via the homotopy perturbation method (HPM) for small as well as moderately large Reynolds numbers. The convergence of the obtained RPM solution is carefully analyzed. Finally, the validity of results is verified by comparing with numerical methods and existing numerical results. Findings - Close agreement of the two sets of results is observed, thus demonstrating the accuracy of the HPM approach for the particular problem considered. Originality/value - Interesting conclusions which can be drawn from this study are that HPM is very effective and simple compared to the existing solution method, able to solve problems without using Pade approximants and can therefore be considered as a clear advantage over the N.M. Bujurke and Phan-Thien techniques.
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    A New Approach to Van der Pol's Oscillator Problem
    (Verlag Z Naturforsch, 2011) Khan, Yasir; Madani, M.; Yildirim, A.; Abdou, M. A.; Faraz, Naeem
    In this paper, we will consider the Laplace decomposition method (LDM) for finding series solutions of nonlinear oscillator differential equations. The equations are Laplace transformed and the nonlinear terms are represented by He's polynomials. The solutions are compared with the numerical (fourth-order Runge-Kutta) solution and the solution obtained by the Adomian decomposition method. The suggested algorithm is more efficient and easier to handle as compared to the numerical method. The results illustrate that LDM is an appropriate method in solving the highly nonlinear equations.
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    A new fractional analytical approach via a modified Riemann-Liouville derivative
    (Pergamon-Elsevier Science Ltd, 2012) Khan, Yasir; Wu, Qingbiao; Faraz, Naeem; Yildirim, A.; Madani, M.
    This work suggests a new analytical technique called the fractional homotopy perturbation method (FHPM) for solving fractional differential equations of any fractional order. This method is based on He's homotopy perturbation method and the modified Riemann-Liouville derivative. The fractional differential equations are described in Jumarie's sense. The results from introducing a modified Riemann-Liouville derivative in the cases studied show the high accuracy, simplicity and efficiency of the approach. (C) 2011 Elsevier Ltd. All tights reserved.