in this paper, a boussinesq equation is solved by using the adomian's decomposition method, modified adomian's decomposition method and homotopy analysis method. the approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. the existence and uniqueness of the solution and the convergence of the propose...

Many time-varying phenomena of various fields in science and engineering can be modeled as a stochastic differential equations, so investigation of conditions for existence of solution and obtain the analytical and numerical solutions of them are important. In this paper, the Adomian decomposition method for solution of the stochastic differential equations are improved.  Uniqueness and converg...

in this paper, we use modified laplace decomposition method to solving initial value problems (ivp) of the second order ordinary differential equations. theproposed method can be applied to linear and nonlinearproblems

The application of a new modified Adomian decomposition method for obtaining the analytic solution of Lane-Emden type equations is investigated. The proposed method, called the spectral Adomian decomposition method, is based on a combination of spectral method and Adomian decomposition method. A comparative study between the proposed method and Adomian decomposition method is presented. The obt...

Adomian decomposition method (ADM) is applied to approximately solve stochastic fractional integrodifferential equations involving nonlocal initial condition. The convergence of the ADM for the considered problem is proved. The mean square error between approximate solution and accurate solution is also given. [Mahmoud M. El-Borai, M.A.Abdou, Mohamed Ibrahim M. Youssef. On Adomian’s Decompositi...

In [M.M. Hosseini, Adomian decomposition method with Chebyshev polynomials, Appl. Math. Comput., in press] an efficient modification of the Adomian decomposition method was presented by using Chebyshev polynomials. Also, in [M.M. Hosseini, Adomian decomposition method for solution of differential algebraic equations, J. Comput. Appl. Math., in press] solution of linear differential algebraic eq...

In this paper, we propose a new variation of the Adomian polynomials, which we call the degenerate Adomian polynomials, for the power series solutions of nonlinear ordinary differential equations with nonseparable nonlinearities. We establish efficient algorithms for the degenerate Adomian polynomials. Next we compare the results by the Adomian decomposition method using the classic Adomian pol...

The population growth, is increase in the number of individuals in population and it depends on some random environment effects. There are several different mathematical models for population growth. These models are suitable tool to predict future population growth. One of these models is logistic model. In this paper, by using Feynman-Kac formula, the Adomian decomposition method is applied to ...

‎‎In this article‎, ‎a new method is introduced to give approximate solution to Van der Pol equation‎. ‎The proposed method is based on the combination of two different methods‎, ‎the spectral Adomian decomposition method (SADM) and piecewise method‎, ‎called the piecewise Adomian decomposition method (PSADM)‎. ‎The numerical results obtained from the proposed method show that this method is an...

the burgers’ equation is a simplified form of the navier-stokes equations that very well represents their non-linear features. in this paper, numerical methods of the adomian decomposition and the modified crank – nicholson, used for solving the one-dimensional burgers’ equation, have been compared. these numerical methods have also been compared with the analytical method. in contrast to...