The Adomian’s decomposition method (ADM) is a solution method with a wide range of applications including the solution of algebraic, differential, integral and integro-differential equations or system of equations. This method was first introduced by Adomian [1, 2] in the beginning of the 1980’s. In this method the solution is considered as an rapidly converging, infinite series. The convergenc...

In this paper, we apply homotopy analysis method (HAM) for computing the eigenvalues of SturmLiouville problems. The parameter h, in this method, helps us to adjust and control the convergence region. The results show that this method has validity and high accuracy with less iteration number in compare to Variation Iteration Method (VIM) and Adomian decomposition method (ADM). Moreover it is il...

In this paper, we use the optimal homotopy analysis method (OHAM) for approximate solutions of the fractional order Logistic equation. The numerical results obtained are compared with the results obtained by using variational iteration method (VIM) and Adomian decomposition method (ADM). The fractional derivatives are described by Caputo's sense. Exact and/or approximate analytical solutions of...

Fuzzy differential equations are used in modeling problems in science and engineering. For instance, it is known that the knowledge of dynamical systems modeled by ordinary differential equations is often incomplete or vague. While, fuzzy differential equations represent a proper way to model dynamical systems under uncertainty and vagueness. In this paper, two methods for solving first order l...

In this Paper, HomotopyPerturbation method (HPM) which is one of the most recent approximate analytical solutions is implemented to solve diffusion-convection-reaction equations (DCRE). The calculations are carried out for two different types of DCRE’s such as the Black-Scholes equation used in financial market option pricing and FokkerPlanck equation from plasma physics. The behavior of the ap...

The Adomian Decomposition Method (ADM) is employed in this paper to investigate the free vibrations of the uniform cracked Euler-Bernoulli beams. The proposed ADM method can be used to analyze the vibration of beams consisting of an arbitrary number of cracks through a recursive way. Based on the ADM and employing some simple mathematical operations, the natural frequencies and the correspondin...

In this work, the homotopy perturbation method (HPM), variational iteration method (VIM) and Adomian decomposition method (ADM) are applied to solve the Rosenau–Hyman equation. We used the initial condition ( u(x, 0) = −83 cos 2 ( x 4 )) for aforementioned methods. Numerical solutions obtained by these methods are compared with the exact solutions, revealing that the obtained solutions are of h...

This article presents an iterative scheme for solution of the viscous Cahn-Hilliard equation. The procedure is based on the Variational Iteration Method (VIM) in which the solutions are calculated in the form of a convergent series with easily computable components. A good agreement is observed between the present solutions and that obtained by other iterative methods like Adomian Decomposition...

This paper examines the solution of a damped beam equation whose damping characteristics are well-defined by the fractional derivative (FD). Homotopy Analysis Method (HAM) is applied for calculating the dynamic response (DR). Unit step and unit impulse functions are deliberated for this analysis. Acquired results are illustrated to show the movement of the beam under various sets of parameters ...

where 3 2 ( , , ) , ( , ) x y z a b ∈ ∈ R R . It is a quadratic and Lorenz-like model.The integrability [9], the limit cycles [10], the chaos synchronization [11] and the feedback controller [12] et al., have been discussed very recently. Many researchers have made much effort to analytical and numerical methods for solving the chaotic systems. For example, the variational iteration method (VIM...