Iterative Methods For Solving Nonlinear Lane-Emden Equations]{Iterative Methods For Solving Nonlinear Lane-Emden Equations

Öz

In this paper we derive solutions for the nonlinear Lane-Emden type of equations with iterative methods, Daftardar-Jafari Method (DJM), Adomian Decomposition Method (ADM) and Differential Transform Method (DTM). The difficulty of Lane-Emden type of equations for implementing these iterative methods is due to the singularity at $x = 0$. We compare the efficiency of DJM - which is the authentic part of the paper - with ADM and DTM in solving the nonlinear, singular, initial value Lane-Emden type of equations.

Anahtar Kelimeler

• Lane-Emden,Daftardar-Jafari,Adomian Decomposition

Kaynakça

1. 1. Adomian, G. (1986) Nonlinear Stochastic OperatorEquations, Academic Press, New York
2. 2. Zhou, J.K. (1986) Differential Transformation and ItsApplications for Electrical Circuits (in Chinese), Huazhong Univerity Press, China
3. 3. Daftardar-Gejji, V. and Jafari, H. (2006) An Iterative MethodFor Solving Nonlinear Functional Equations, Journal of Mathematical Analysisand Applications 316, 753-763
4. 4. Bhalekar, S., Daftardar-Gejji, V. (2011) Convergence of theNew Iterative Method, International Journal of Differential Equations,Vol:2011, 1-10
5. 5. Wazwaz, A.M. (2001) A New Algorithm For SolvingDifferential Equations of Lane-Emden Type, Applied Mathematics and Computation118, 287-310
6. 6. Wazwaz, A.M., Rach, R. (2011) Comparison of the AdomianDecomposition Method And The Variational Iteration Method For Solving theLane-Emden Equations of The First And Second Kinds, Kybernetes, Vol. 40, No.9/10, 1305-1318
7. 7. Mukherjee, S., Roy, B., Chaterjee, P.K (2011) Solution ofLane-Emden Equation by Differential Transform Method, International Journal ofNonlinear Science, Vol.12, No.4, 478-484
8. 8. Khan, Y., Svoboda, Z., Smarda, Z. (2012) Solving CertainClasses of Lane-Emden Type of Equations Using The Differential TransformationMethod, Advances in Difference Equations, https://doi.org/10.1186/1687-1847-2012-174

9. 9. Wazwaz, A.M., Rach, R., Duan, J.S. (2013) A Study OnThe Systems of Voltera Integral Forms of The Lane-Emden Equations By TheAdomian Decomposition Method, Mathematical Methods In The Applied Science,DOI: 10.1002/mma.2776
10. 10. Cherruault, Y., Adomian, G., Abbaoui, K. and Rach, R.(1995) Further Remarks on Convergence of Decomposition Method, InternationalJournal of Bio-Medical Computing, 38, 89-93
11. 11. Hosseini, M. M., Nasabzadeh, H. (2006) On the Convergence ofAdomian Decomposition Method, Applied Mathematics and Computation, 182, 536-543
12. 12. Adomian, G. (1984) On the Convergence Region forDecomposition Solutions, Journal of Computational and Applied Mathematics, 11, 379-380
13. 13. Chandrasekhar, S. (1967) An Introduction To the Study of Stellar Structure, Dover, New York, p.91 - 95