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2 International Journal of Applied Mechanics and Engineering

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Application of Adomian Decomposition Method and Variational Iteration Method for the solution of a fractional (arbitrary) order differential equation

100%

Ray S. S. , Bera R. K.

tom Vol. 14, no 4

1169-1173

In this paper, the Adomian decomposition method (ADM) and variational iteration method (VIM) are implemented to obtain an approximate solution to a fractional differential equation with an arbitrary order […]. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions to different types of differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. The approximate solution obtained using the VIM is exactly the same and in good agreement as that obtained by using the ADM.

Nonperturbative analytical solution of the time fractional advection problem

80%

Sutradhar T. , Datta B. K. , Bera R. K.

tom Vol. 17, no. 2

629-636

A nonperturbative analytic solution is derived for the time fractional nonlinear advection problem by using Adomian's Decomposition Method (ADM). The solution is obtained in the form of a power series with easily computable coefficients. The present method performs extremely well in terms of accuracy, efficiency and simplicity.