the work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on homotopy analysis method  and adomian decomposition method for solving  differential equations of integer and fractional orders.

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

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...

reduced differental transform method (rdtm), which isone of the useful and effective numerical method, is applied to solve nonlinear time-dependent foam drainage equation (fde) with different initial conditions. we compare our method with the famous adomian decomposition and laplace decomposition methods. the obtained resultsdemonstrated that rdtm is a powerful tool for solving nonlinear par...

in this paper, we conduct a comparative study between the homotopy perturbation method (hpm) and adomian’s decomposition method (adm) for analytic treatment of nonlinear volterra integral equations, and we show that the hpm with a specific convex homotopy is equivalent to the adm for these type of equations.

in this work, the solution of a boundary value problem is discussed via asemi analytical method. the purpose of the present paper is to inspect theapplication of the adomian decomposition method for solving the nagumotelegraph equation. the numerical solution is obtained for some special casesso that demonstrate the validity of method.

n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.

a 2-d heat conduction model has been solved by using the adomian decomposition method topredict the transient temperature and heat flux distribution in a thick solid that is irradiated by a laser source.the laser source may operate in a continuous wave (cw) mode or repeated pulse (rp) mode and may havearbitrary, spatial and temporal profiles.a generalized solution containing five-terms approxim...

we introduce and discuss the homotopy perturbation method, the adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. then, we give an example of the stefan problem with  kinetics and solve it by these methods.