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Approximate Analytical Solutions of the Regularized Long Wave Equation Using the Optimal Homotopy Perturbation Method [PDF]
The Scientific World Journal, 2014 The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations.
Constantin Bota, Bogdan Căruntu
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Linearized Homotopy Perturbation Method for Two Nonlinear Problems of Duffing Equations
Journal of Mathematics Research, 2021 In the paper, we solve two nonlinear problems related to the Duffing equations in space and in time. The first problem is the bifurcation of Duffing equation in space, wherein a critical value of the parameter initiates the bifurcation from a trivial ...
Chein‐Shan Liu
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Journal of Low Frequency Noise, Vibration and Active Control, 2021 This paper couples Li–He’s homotopy perturbation method with the energy method to obtain an approximate solution of a tangent nonlinear packaging system.
Qiu-Ping Ji +3 more
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Two Modifications of the Homotopy Perturbation Method for Nonlinear Oscillators [PDF]
Journal of Applied and Computational Mechanics, 2020 Nonlinear vibration arises in engineering and physics, and the periodic motion of these nonlinear oscillatory systems have rich dynamics. An estimation of amplitude-frequency relationship of a nonlinear oscillator is much needed, therefore, well-known ...
Naveed Anjum, Ji-Huan He
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Homotopy perturbation method with an auxiliary parameter for nonlinear oscillators
Journal of Low Frequency Noise, Vibration and Active Control, 2019 A brief introduction to the development of the homotopy perturbation method is given, and the main milestones are elucidated with more than 90 references.
Dan-Ni Yu, Ji-Huan He, Andres G Garcıa
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Desimal, 2021 The variational homotopy perturbation method is developed by combining variational iteration method and homotopy perturbation method. Variational iteration method has an efficient process in solving a wide variety of equations and systems of equations ...
Atika Faradilla +3 more
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A GOOD INITIAL GUESS FOR APPROXIMATING NONLINEAR OSCILLATORS BY THE HOMOTOPY PERTURBATION METHOD
Facta Universitatis, Series: Mechanical Engineering, 2023 A good initial guess and an appropriate homotopy equation are two main factors in applications of the homotopy perturbation method. For a nonlinear oscillator, a cosine function is used in an initial guess.
Jihuan He +2 more
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Python approach for using homotopy perturbation method to investigate heat transfer problems
Case Studies in Thermal EngineeringPayam Jalili +5 more
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The Aboodh transformation-based homotopy perturbation method: new hope for fractional calculus
Frontiers of Physics, 2023 Fractional differential equations can model various complex problems in physics and engineering, but there is no universal method to solve fractional models precisely.
Huiqiang Tao, N. Anjum, Yong-Ju Yang
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Proceedings of the Royal Society A, 2023 The exploration of collisional fragmentation pheno-mena remains largely unexplored, yet it holds considerable importance in numerous engineering and physical processes.
Nisha Yadav +4 more
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