Application of Adomian Decomposition Method to Solving Higher Order Singular Value Problems for Ordinary Differential Equations

Abstract

This paper is an attempt to solve singular value problems for higher order ordinary differential equation by using new modification of Adomian Decomposition Method (ADM). Convergent series solution of considered problem have been obtained. Three numerical examples are discussed to validate the strength and ease of the method used.

Entropy generation effect of a buoyancy force on hydromagnetic heat generating couple stress fluid through a porous medium with isothermal boundaries

“…The preference for this approach is to accelerate the rapid convergence and does not demand any linearization, discretization, use of guess or perturbation and drastically reduce the number of iterations as mentioned in [26]. The abundance of knowledge on the series solution (ADM) from literature [27,28,29,30,31,32] has been proved to be efficient, reliable, and as an alternative powerful tool in providing solution to differential and integral equations and hence, reduce computational volume. The estimation on the quality of being genuine of the ordered solution and its convergence were ascertained in tables, shown in the discussion section, concerning the already accomplished discoveries in [6,10] where perturbation method was utilized and examined justifiably with other thermophysical parameters existing in the flow system.…”

Adomian method for solving Emden-Fowler equation of higher order

“…So if we continue finding values of y, we will get the right solution. y(0) = y (0) = y (0) = y (0) = y (4) (0) = y (5) (0) = y (6) (0) = 0, y(x) = x 7 is the solution of eq. (4.9).…”

“…Adomian method is considered as one of the most effective methods in finding convergence solutions as well as the complete solution. As it started by George Adomian in 1980s [1][2][3][4], many suggested amendments were presented on this method as in [5,7]. Our target in this work is to find a solution of the equation under study.…”

Variational Iteration Method for Analytical Solution of the Lane-Emden Type Equation with Singular Initial and Boundary Conditions

“…The numerical solution of the Lane-Emden equation (3) as well as other types of linear and nonlinear singular IVPs in quantum mechanics and astrophysics [5,6], is numerically challenging because of the singularity behavior at the origin. Hasan and Zhu [7,8] have solved such a singular initial value problem by the Taylor series and modified Adomian decomposition methods. Gupta and Sharma [9] have also used the Taylor series method to solve Lane-Emden and Emden-Fowler equations.…”