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Dergiler / International Journal of Advances in Engineering and Pure Sciences / 2026 / Cilt: 30 Sayı: 2

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

Faruk Uçar(Marmara University)
Volkan Yaman(Marmara University)
Bülent Yılmaz(Marmara University)
Sayfa
176–188
Yayın Tarihi
2018-06-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

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Amaç & Hipotez: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).
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Temel Bulgular & Veri:The difficulty of Lane-Emden type of equations for implementing these iterative methods is due to the singularity at $x = 0$.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Lane-Emden · Daftardar-Jafari · Adomian Decomposition

Özet

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.

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.

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Bu Makaleye Atıf Yap

Uçar, F., Yaman, V., Yılmaz, B. (2018). Iterative Methods For Solving Nonlinear Lane-Emden Equations]{Iterative Methods For Solving Nonlinear Lane-Emden Equations. International Journal of Advances in Engineering and Pure Sciences, Cilt: 30 Sayı: 2, 176–188. https://doi.org/10.7240/marufbd.410960

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Kaynakça (13)

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  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
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  13. Chandrasekhar, S. (1967) An Introduction To the Study of Stellar Structure, Dover, New York, p.91 - 95