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

Main Article Content

Yahya Qaid Hasan
Somaia Ali Alaqel


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.

Ordinary differential equations, adomian decomposition method, higher-order singular initial value problems.

Article Details

How to Cite
Hasan, Y. Q., & Alaqel, S. A. (2020). Application of Adomian Decomposition Method to Solving Higher Order Singular Value Problems for Ordinary Differential Equations. Asian Journal of Probability and Statistics, 9(4), 22-28.
Original Research Article


Kutniv MV, Datsko BY, Wloch A. A new approach to constructing of explicit one-step methods of higher order for singular initial value problems for nonlinear ordinary differential equations.

Appl Numer Math; 2019. Available:

Rufai MA, Ramos H. Numerical solution of second-order singular problems arising in astrophysics by combining apair of one-step hybrid block Nystrm methods. Astrophys Space Sci; 2020. Available:

Roul P, Goura VP, Agarwal R. Acompact finite difference method for general class of nonlinear singular boundary value problems with Neumann and Robin boundary conditions. Appl Math Compute. 2019;350:283-304.

Shiralashetti SC, Deshi AB, Desai PB. Haar wavelet collocation method for the numerical solution of singular initial value problems. Ain Shams Eng J. 2016;7(2): 663670.

Yildirim A, zis T. Solutions of singular IVPs of Lane-Emden type by the variational iteration method. Nonlinear Anal : A Theory Methods Appl. 2009;70:24802484.

Alderremy AA, Elzaki TM, Chamekh M. Modified adomian decomposition method to solve generalized emden-fowler systems for singular IVP. Mathematical Problems in Engineering; Available:

Alaqel SA, Hasan YQ. A new application of Adomian Decomposition method. IOSR-JM. ;16:11-15.

Biazar J, Hosseini K. A modified adomian decomposition method for singular initial value Emden-fowler type equations. Int J Appl Math Research. 2016;5(1):69-72.

Hasan YQ, Zhu LM. Modified Adomian decomposition method for singular initial value problems in the second-order ordinary differential equations. Surv Math Appl. 2008;3:183-193.

Umesh, Kumar M. Numerical solution of singular boundary value problem using advanced Adomian decomposition method. Eng Comput; 2020. Available:

Wazwaz AM, Rach R, Duan JS. Solving new fourth-order Emden-Fowler type equations by the Adomian Decomposition method. Int J Comput Meth Eng Sci Mech; 2015. Available:

Wazwaz AM. A reliable treatment of singular Emden-Fowler initial value problems and boundary value problems. Appl Math Comput. 2011;217(24):10387-10395.

Adomian G. A review of the decomposition in applied and some recent results for nonlinear equation. Math Comput Model. 1999;13:17-43.

Adomian G. Solving frontier problem of physics: The decomposition method. Kluwer academic publishers London; 1994.

Alaqel SA, Hasan YQ. The general solution for singular equations of (n+1) order using Adomian decomposition method. J Math Comput Sci. 2020;6: 2261-2281.

Dabwan NM, Hasan YQ. Using Adomian decomposition method in solving fractional LaneEmden type equations. R A Journal. 2020;3(8):274-283.