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The solution of multipoint boundary value problems by the Optimal Homotopy Asymptotic Method

Computers and Mathematics With Applications, 2010
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Saeed Islam, Javed Ali
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The Optimal Homotopy Asymptotic Method for solving Blasius equation

Applied Mathematics and Computation, 2014
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Vasile Marinca, Nicolae Herisanu
exaly   +4 more sources

Comparison between homotopy perturbation method and optimal homotopy asymptotic method for the soliton solutions of Boussinesq–Burger equations

Computers and Fluids, 2014
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S Saha Ray
exaly   +3 more sources

Application of the optimal homotopy asymptotic method for solving a strongly nonlinear oscillatory system

Mathematical and Computer Modelling, 2013
Abstract In this paper, the optimal homotopy asymptotic method (OHAM) and the traditional homotopy analysis method (HAM) are used to obtain analytical solution for a strongly nonlinear oscillation. Moreover, the homotopy-pade technique is employed to accelerate the convergence of solution series of traditional HAM.
Khosro Sayevand, Mojtaba Fardi, Ahmad Golbabai   +2 more
exaly   +2 more sources

Optimal Homotopy Asymptotic Method

2015
The notion of homotopy is an important part of topology and thus of differential geometry. The homotopy continuation method or shortly speaking homotopy was known as early as in the 1930s. Thus, in 1892, Lyapunov [1] introduced the so-called “artificial small parameters method” considering a linear differential equation with variable coefficients in ...
Vasile Marinca, Nicolae Herisanu
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Optimal homotopy asymptotic and multistage optimal homotopy asymptotic methods for Abel Volterra integral equation of the second kind

2020
Summary: In this paper, optimal homotopy asymptotic method (OHAM) and multistage optimal homotopy asymptotic (MOHAM) method are applied to find an approximate solution to Abel's integral equation, that is in fact a weakly singular Volterra integral equation. To illustrate these approaches one example is presented. The results confirm the efficiency and
Biazar, Jafar, Montazeri, Roya
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Optimal Homotopy Asymptotic Method for Solving a Nonlinear Problem in Elasticity

2012 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2012
In this paper a homotopy approach, called the optimal homotopy asymptotic method (OHAM) is presented as a new and powerful technique for analytical treatment of a nonlinear problem related to the stress and deformation state of a thin elastic plate. This technique combines the features of the homotopy concept with an efficient computational algorithm ...
Remus-Daniel Ene, Vasile Marinca, Romeo Negrea, Bogdan Caruntu   +3 more
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The comparison between Homotopy Analysis Method and Optimal Homotopy Asymptotic Method for nonlinear age-structured population models

Communications in Nonlinear Science and Numerical Simulation, 2012
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Ghoreishi, M., Ismail, A. I. B. Md., Alomari, A. K., Bataineh, A. Sami   +3 more
exaly   +3 more sources

The Third Alternative of the Optimal Homotopy Asymptotic Method

2015
In this chapter, we consider m = 2 into Eq. 2.29 such that we obtain the second-order approximate solution in the form $$ \overline{u}\left(x,{C}_i\right)={u}_0(x)+{u}_1\left(x,{C}_i\right)+{u}_2\left(x,{C}_i\right) $$ where the terms u0, u1 and u2 are given by the linear differential equations 2.19, 2.20, 2.23, 2.25 and 2.26 respectively or ...
Vasile Marinca, Nicolae Herisanu
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Comparison between homotopy analysis method and optimal homotopy asymptotic method for nth-order integro-differential equation

Mathematical Methods in the Applied Sciences, 2011
Summary: This paper presents a general framework for solving an \(n\)th-order integro-differential equation using homotopy analysis method (HAM) and optimal homotopy asymptotic method (OHAM). OHAM is parameter free and can provide better accuracy over the HAM at the same order of approximation.
Abedel-Karrem Alomari
exaly   +3 more sources