Results 11 to 20 of about 2,716 (179)
The essence of the homotopy analysis method [PDF]
Applied Mathematics and Computation, 2010 The generalized Taylor expansion including a secret auxiliary parameter $h$ which can control and adjust the convergence region of the series is the foundation of the homotopy analysis method proposed by Liao. The secret of $h$ can't be understood in the frame of the homotopy analysis method. This is a serious shortcoming of Liao's method. We solve the
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A computational approach for fractional convection-diffusion equation via integral transforms
Ain Shams Engineering Journal, 2018 In this paper, two efficient analytic techniques namely the homotopy analysis transform method (HATM) and homotopy perturbation Sumudu transform method (HPSTM) are implemented to give a series solution of fractional convection-diffusion equation which ...
Jagdev Singh, Ram Swroop, Devendra Kumar
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An analytical approach for the nonlinear forced vibration of clamped-clamped buckled beam [PDF]
Journal of Theoretical and Applied Vibration and Acoustics, 2017 Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framework for verification of numerical results.
Shahin Mohammadrezazadeh +2 more
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Ain Shams Engineering Journal, 2016 In this article, an analysis has been performed to study the two dimensional viscous flow between slowly expanding and contracting walls with weak permeability.
E. Rahimi +4 more
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مجلة بغداد للعلوم, 2022 An efficient modification and a novel technique combining the homotopy concept with Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced in this paper . Both
Khalid Hammood AL-Jizani +1 more
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Journal of Low Frequency Noise, Vibration and Active Control, 2019 In this paper, we study the dynamical behaviors of coupled nonlinear systems with delay coupling by the multiple scales method and the homotopy analysis method.
Youhua Qian, HX Fu, JM Guo
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The homotopy analysis method for q-difference equations
Ain Shams Engineering Journal, 2018 The q-difference equations are kind of important problems in q-calculus and applied mathematics. In this paper, the homotopy analysis method is extended to find approximate solution for some of q-differential equations.
Mourad S. Semary, Hany N. Hassan
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Homotopy analysis transform algorithm to solve time-fractional foam drainage equation
Nonlinear Engineering, 2016 This paper emphasizes on finding the solution for a foam drainageequation using the technique of modified homotopy analysis transform method (MHATM). MHATM is a new amalgamation of the homotopy analysis method and Laplace transform method with homotopy ...
Singh Mukesh +3 more
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Solve the Initial Value Problems of Fractional Order Using The Homotopy Analytical Method and Improve Them Using Pade' Approximations [PDF]
مجلة التربية والعلم, 2019 In this research , the initial value problems of the caputo- fractional order are solved using the homotopy analysis method. The Pade' approximation is added to the fractional order to improve this method.
Heba Mahmmood, Kais Ibraheem
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Results in Physics, 2016 The main aim of this paper is to propose a new and simple algorithm namely the optimal q-homotopy analysis method (Oq-HAM), to obtain approximate analytical solutions of the convection diffusion (CD) equation.
Mohamed S. Mohamed, Yasser S. Hamed
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