Analytic Solution of Nonlinear Boundary-Value Problems in Several Dimensions by Decomposition

Modeling the spread of computer virus via Caputo fractional derivative and the beta-derivative

“…This accounts for the reasons why in recent times, a lot of attention has been devoted in the quest for obtaining techniques that can ensure asymptotic solutions in such situations. We shall make reference to some of the recent techniques on this subject which are efficient and effective and have been widely used; for instance, the decomposition method [12], Sumudu homotopy perturbation method [20], the Adomian Decomposition method [11,21], homotopy perturbation method [19,22,23], the homotopy Laplace perturbation method [24], and the homotopy. In this study however, we shall make use of two of these stated techniques, specifically the Laplace homotopy perturbation method and the homotopy decomposition method.…”

Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative

“…That is why in the recent decades, several studies have been done in order to build some analytical techniques that can be used to provide asymptotic solutions in such systems. We shall mention some of the recent and efficient ones that have been intensively used, such as the homotopy perturbation method [11,13], the Adomian Decomposition method [14,15], the homotopy Laplace perturbation method [16], the Sumudu homotopy perturbation method [17] and the homotopy decomposition method [18]. However, in this paper we shall use only two of these mentioned techniques, namely the Laplace homotopy perturbation method and the homotopy decomposition method.…”

Pulse Propagation in a Non-Linear Medium

“…In order to obtain the analytical solution of the equation (4) the Adomian method is used, where G is a nonlinear operator from a Hilbert space H into H, p is a given function in H. In the solution f satisfies (4) and it is assumed that (4) has a unique solution for every p belonging to H. The Adomian method consists in representing f as follows [4][5][6][7][8] …”

“…This paper considers the use of the Adomian decomposition method for solving the NLSE for pulse propagation in non-linear media. It has previously been used to solve a wide range of physical problems [4][5][6][7] and is a semi-exact method which does not require linearization or discretization. The method has gone through a series of modification in the following references [8][9][10][11][12][13][14][15][16].…”