Solving Singular Bvps Ordinary Differential Equations By Modified Homotopy Perturbation Method

Abstract

In this paper, we use modified homotopy perturbation method to solving singular boundary value problems (BVP) of higher-order ordinary differential equations. The proposed method can be applied to linear and nonlinear problems.The results prove that the modified HPM is a powerful tool for the solution of singular BVPs.

Adomian Decomposition Method For Solving Fractional Bratu-type Equations

“…Therefore several methods for the approximate solutions to classical differential equations [11] are extended to solve differential equations of fractional order numerically. These methods include, Adomian decomposition method [12], homotopy perturbation method [13][14][15][16], homotopy analysis method [17], variational iteration method [18], generalized differential transform method [19], finite difference method [20] and etc [21,22].…”

General solution of second order fractional differential equations

“…Due to this fact, finding an approximate solution of fractional differential equations is clearly an important task. In recent years, many effective methods have been proposed for the approximate solution fractional differential equations, such as Adomian decomposition method [3,4], homotopy perturbation method [5][6][7][8], homotopy analysis method [9,10], variational iteration method [11], generalized differential transform method [12] and other methods [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The organization of the paper is as follows: In Section 2, Basic definitions, such as conformable fractional derivative, and conformable fractional integral, will be presented.…”

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].…”