Research Article
Iterative Methods For Solving Nonlinear Lane-Emden Equations]{Iterative Methods For Solving Nonlinear Lane-Emden Equations
Abstract
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.
References
- 1. Adomian, G. (1986) Nonlinear Stochastic OperatorEquations, Academic Press, New York
- 2. Zhou, J.K. (1986) Differential Transformation and ItsApplications for Electrical Circuits (in Chinese), Huazhong Univerity Press, China
- 3. Daftardar-Gejji, V. and Jafari, H. (2006) An Iterative MethodFor Solving Nonlinear Functional Equations, Journal of Mathematical Analysisand Applications 316, 753-763
- 4. Bhalekar, S., Daftardar-Gejji, V. (2011) Convergence of theNew Iterative Method, International Journal of Differential Equations,Vol:2011, 1-10
- 5. Wazwaz, A.M. (2001) A New Algorithm For SolvingDifferential Equations of Lane-Emden Type, Applied Mathematics and Computation118, 287-310
- 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. 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. 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. 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. 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. Hosseini, M. M., Nasabzadeh, H. (2006) On the Convergence ofAdomian Decomposition Method, Applied Mathematics and Computation, 182, 536-543
- 12. Adomian, G. (1984) On the Convergence Region forDecomposition Solutions, Journal of Computational and Applied Mathematics, 11, 379-380
- 13. Chandrasekhar, S. (1967) An Introduction To the Study of Stellar Structure, Dover, New York, p.91 - 95
Iterative Methods For Solving Nonlinear Lane-Emden Equations]{Iterative Methods For Solving Nonlinear Lane-Emden Equations
Abstract
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.
References
- 1. Adomian, G. (1986) Nonlinear Stochastic OperatorEquations, Academic Press, New York
- 2. Zhou, J.K. (1986) Differential Transformation and ItsApplications for Electrical Circuits (in Chinese), Huazhong Univerity Press, China
- 3. Daftardar-Gejji, V. and Jafari, H. (2006) An Iterative MethodFor Solving Nonlinear Functional Equations, Journal of Mathematical Analysisand Applications 316, 753-763
- 4. Bhalekar, S., Daftardar-Gejji, V. (2011) Convergence of theNew Iterative Method, International Journal of Differential Equations,Vol:2011, 1-10
- 5. Wazwaz, A.M. (2001) A New Algorithm For SolvingDifferential Equations of Lane-Emden Type, Applied Mathematics and Computation118, 287-310
- 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. 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. 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. 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. 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. Hosseini, M. M., Nasabzadeh, H. (2006) On the Convergence ofAdomian Decomposition Method, Applied Mathematics and Computation, 182, 536-543
- 12. Adomian, G. (1984) On the Convergence Region forDecomposition Solutions, Journal of Computational and Applied Mathematics, 11, 379-380
- 13. Chandrasekhar, S. (1967) An Introduction To the Study of Stellar Structure, Dover, New York, p.91 - 95
There are 13 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Article |
| Authors | |
| Acceptance Date | June 29, 2018 |
| Publication Date | June 30, 2018 |
| DOI | https://doi.org/10.7240/marufbd.410960 |
| IZ | https://izlik.org/JA87KP96JR |
| Published in Issue | Year 2018 Volume: 30 Issue: 2 |
Cite
Marmara Journal of Pure and Applied Sciences
e-ISSN : 2146-5150