### Adjusted Adomian Decomposition Method for Solving Emden-Fowler Equations of Various Order

#### Abstract

#### Full Text:

PDF#### References

G. Adomian, A review of the decomposition in applied mathematics. Mathematical analysis and applications., 135(1988),501-544.

G. Adomian, A review of the decomposition method and some recent results for nonlinear equations, Computers Math. Applic. 21(1991), 101-127.

G. Adomian , R Rach, Inversion of nonlinear stochastic operators, J.Math.Anal,Appl.91(1983),39-46.

G. Adomian , Solving FrontierProblems of Physics:The Decomposition Method , Kluwer academic publishers, London.(1994)

E.U Agom , A.M Badmus, Application of Adomian Decomposition Method in Solving Second Order Nonlinear Ordinary Differential Equations , International Journal of Engineering Science Invention 4(2015)60-65.

H.A. Alkresheh , New classes of Adomian polynomials for the Adomian decomposition method , International Journal of Engineering Science Invention 5(2016)37-44.

M.Al-Mazmumy and H. Al-Malki, SOME MODIFICATIONS OF ADOMIAN DECOMPOSITION METHODS FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS, IJRRAS 23 (2015) ,164-173.

E.A. Az-Zo'bi, Modified Adomian-Rach Decomposition Method for Solving Nonlinear Time-Dependent IVPs, Applied Mathematical Sciences, 11(2017) 387 – 395.

J. Biazar, K. Hosseini, A modified Adomian decomposition method for singular initial value Emden-Fowler type equationsInternational Journal of Applied Mathematical Research, 5 (1) (2016) 69-72

L.Bougoffa, S. Mziou and R.C. Rach, Exact and Approximate Analytic Solutions of theJeffery-Hamel Flow Problem by the Duan-Rach Modified Adomian Decomposition Method, MathematicalModelling and Analysis, 21( 2), 2016, 174-187

S. Chandrasekhar, An introduction to the study of stellar structure, Dover publications, New York, (1967).

H.T. Davis, Introduction to nonlinear differential and integral equations, Dover publications, NewYork, (1962).

M, Dehghan, F. Shakeri, Approximate solution of a differential equation arising in astrophysics using the variational iteration method, New Astronomy,13 (2008),53-59.

J.S. Duan , R Rach, A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations. Appl. Math. Comput., 218(2011),4090–4118.

J. Duan , The Adomian Polynomials and the New Modified Decomposition Method for BVPs of nonlinear ODEs , Mathematical Computation March 4(2015)1‐6.

S. E .Fadugba, S. C. Zelibe, Edogbanya O. H. On the Adomian Decomposition Method for the solution of Second Order Ordinary Differential Equations , International Journal of Mathematics and Statistics Studies 1(2013) 20-29.

R.H. Fowler, Further studies of Emdens and similar differential equations, Quarterly Journal of Mathematics, 2(1) (1931), 259-288.

Y. Q. Hasan, L. M. Zhu, Modified Adomian decomposition method for singular initial value problems in the second-order ordinary differential equations, Surveys in mathematics and its applications, 3(2008)183-193.

Y. Q. Hasan, Modified Adomian decomposition method for second order singular initial value problems. Advances in Computational Mathematics and its Applications, 1(2012),94-99.

Y. Q. Hasan, A.M.S. Mutaish, Modified Adomian decomposition method for solving higher odd order boundary value problems. MAYFEB Journal of Mathematics, 2(2017), 74-79.

Y. Q. Hasan, A new development to the Adomian decomposition for solving singular IVPs of Lane-Emden Type. United States of America Research Journal (USARJ) 2 (2014) 2332-2160

J.H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Compute, 114(2/3) (2000), 115-123.

K. Parand, M. Shahini, and M. Dehghan, Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type, J. Compute. Phys. 228 (2009), 8830-8840.

R. Rach, J.S. Duan, and A.M. Wazwaz, Solving the Two–Dimensional Lane–Emden Type Equations by the Adomian Decomposition Method, Journal of Applied Mathematics and Statistics 3(2016) 15-26.

A.M.Wazwaz, A new algorithm for calculating Adomian polynomials for nonlinear operators. Appl Math Comput 111(1)(2000)33-51

Wazwaz A. M, A First Course in Integral Equations, World Scientific, Singapore, 1997.

A.M.Wazwaz, Adomian decomposition method for a reliable treatment of the Emden-Fowler equation, Appl. Math. Comput. 161 (2005), 543-560.

A.M.Wazwaz, The variational iteration method for solving nonlinear singular boundary value problems arising in various physical models, Commun. Nonlinear Sci. Numer. Simulat. 16 (2011), 3881-3886.

A.M.Wazwaz, solving two Emden–Fowler type equations of third order by the variational iteration method, Appl. Math. Inf. Sci. 9(2015), 2429-2436.

A.M.Wazwaz, R.Rach, L.Bougoffa and J.S.Duan, Solving the Lane–Emden–Fowler Type Equations of Higher Orders by the Adomian Decomposition Method, CMES, 100(2014)507-529.

A. Yildirim and T .Ozis, Solutions of singular IVPs of Lane Emden type by homotopy perturbation method, Phys. Lett. A 369 (2007), 70-76.

A. Yildirim and T .Ozis, Solutions of singular IVPs of Lane-Emden type by the variational iteration method, Nonlinear Analysis,70 (2009),2480-2484.

N. H. Zomot and O. Y. Ababneh, Solution of Differential Equations of Lane-Emden Type by Combining Integral Transform and Variational Iteration Method, Nonlinear Analysis and Differential Equations, Vol. 4, 2016, no. 3, 143 – 150.

### Refbacks

- There are currently no refbacks.

**MAYFEB Journal of Mathematics**

**Toronto, Ontario, Canada**

**MAYFEB TECHNOLOGY DEVELOPMENT**

**ISSN**

**2371-6193**