Exact Solutions for a Class of Nonlinear Singular Two-Point Boundary Value Problems: The Decomposition Method

Abstract

Many problems in applied mathematics and engineering are usually formulated as singular twopoint boundary value problems. A well-known fact is that the exact solutions in closed form of such problems were not obtained in many cases. In this paper, the exact solutions for a class of nonlinear singular two-point boundary value problems are obtained to the first time by using Adomian decomposition method.

An approach for solving singular two point boundary value problems: analytical and numerical treatment

“…Consider the nonlinear singular two-point boundary value problem [23,24] u (x) + 0.5 x u (x) = e u(x) 0.5 − e u(x) , x ∈ (0, 1),…”

Numerical Treatment of Initial-Boundary Value Problems with Mixed Boundary Conditions

“…Several different resolution techniques for solving BVPs for nonlinear ordinary differential equations by using the ADM were considered by Adomian and Rach [12]- [18], Adomian [19], and Wazwaz [20]- [26]. Also, for a two-point BVP for second-order nonlinear differential equations, Adomian and Rach [17] [18] proposed the double decomposition method in order to avoid solving such nonlinear algebraic equations, and Jang [27] and Ebaid [28] introduced different modified inverse linear operators. Adomian [29] suggested a modified method for the hyperbolic, parabolic and elliptic partial differential equations with initial and boundary conditions by using two equations for u, one inverting the t L operator and the other inverting the x L operator, then, adding them and dividing by two.…”

Solving Two-Points Singular Boundary Value Problem Using Hermite Interpolation

“…Singular boundary value problems are always very important, there exists many method for solving. For example, modified Homotopy perturbation method [4], differential transform method [5], cubic trigonometric B-spline method [6], Adomian decomposition method [7], shooting method [8], variation method [9].…”