Recent Modifications of Adomian Decomposition Method for Initial Value Problem in Ordinary Differential Equations

Abstract

In this paper, some modifications of Adomian decomposition method are presented for solving initial value problems in ordinary differential equations. Also, the restarted and two-step methods are applied to the problem. The effectiveness of the each modified is verified by several examples.

Desulfurization of Model Oil through Adsorption over Activated Charcoal and Bentonite Clay Composites

“…Adsorption isotherms models were also employed to study the mechanism of adsorption. Three models, namely, Langmuir isotherms, Freundlich adsorption model [41][42][43], and Temkin isotherm [44] were applied. Mathematically Langmuir isotherms can be expressed as Eq.…”

Solving the linear homogeneous one-dimensional wave equation using the Adomian decomposition method

“…These 'noise' terms do not appear for homogeneous equations but only for specific types of non-homogeneous equations. Furthermore, it has formally been shown that if some terms in u 0 are cancelled by identical terms in u 1 with opposite signs, even though u 1 includes additional terms, the remaining non-cancelled terms in u 0 constitute the exact solution of the given equation [14,15]. However, it is necessary and essential to verify that the remaining non-canceled terms satisfy the given equation.…”

“…Figure 2 gives the results for 0 < x < 1 and 0 < t < 3. the wave equation. The work of this paper can be improved by (1) using one of the many modifications of the ADM, e.g., [15,16,17], instead of the standard ADM. (2) applying the ADM to the solution of Volterra integro-differential and integral equations that frequently occur in insurance mathematics; (3) applying the method to wave equations with a source term; (4) applying the ADM to partial differential equations with non-linear terms.…”

Irreversibility analysis for a mixed convective flow of a reactive couple stress fluid flow through channel saturated porous materials

“…The coupled nonlinear equations for momentum in (6) and energy in (7) with the boundary conditions in (8) are solved by making use of ADM [17][18][19]. First, the BVP are converted to the integral forms as follows: …”