Murat DÜZ

Fourier Ayrıştırma Metodu ile Lane-Emden Denkleminin Çözümü

Bu makalede Fourier ayrıştırma metodunu kullanarak Lane-Emden tipi denklemlerin bir sınıfının çözümünü elde etmeyi denedik. Bu metot Fourier dönüşümü ve Adomian ayrıştırma metodu (FADM) birlikte kullanılarak elde edilir.

Anahtar Kelimeler:

Fourier Transform, Lane emden equation, Adomian Decomposition Method

Solution of Lane-Emden Equation with Fourier Decomposition Method

In this article, we tried to get the solution of a class of Lane Emden type equations by using the Fourier Decomposition Method. This method is obtained by using the Fourier transform and the Adomian Decomposition method (FADM) together.

Keywords:

Fourier Transform, Lane-Emden equation, Adomian Decomposition Method,

PDF

___

A.M.Wazwaz,“A new algorithm for solving differential equations of Lane-Emden type,” Appl. Math. Comput., 118 (2-3), 287–310, 2001.
S. Mukherjee, B. Roy and P. K.Chaterjee, “Solution of Lane-Emden Equation by Differential Transform Method,” Int. J. Nonlinear Sci., 12 (4), 478-484, 2011.
A. Yıldırım, T. Öziş, “Solutions of singular IVPs of Lane-Emden type by the variational iteration method,” Nonlinear Anal.- Theor., 70 (6), 2480–2484, 2009.
K. Parand, M. Razzaghi, “Rational Legendre approximation for solving some physical problems on semi-infinite intervals”, Phys. Scr., 69(5), 353-357, 2004.
K. Parand, M. Razzaghi,“Rational Chebyshev tau method for solving higher-order ordinary differential equations,” Int. J. Comput. Math., 81(1), 73-80, 2004.
Y. Khan, Z. Svoboda, Z. Smarda, “Solving certain classes of Lane-Emden type equations using the differential transformation method,” Adv.Differ. Equ., 2012(1), 1-11, 2012
M. Yiğider, K. Tabatabaei, E. Çelik, “The Numerical Method for Solving Differential Equations of Lane-Emden Type by Pade Approximation,” Discrete Dyn. Nat. Soc., 2011, 1-9, 2011.
S. G. Hosseini, S. Abbasbandy, “Solution of Lane-Emden type equations by combination of the spectral method and Adomian Decomposition method,” Math. Probl. Eng., 2015, 1-10, 2015.
H. Aminikbah, “Solutions of the Singular IVPs of Lane-Emden type equations by combining Laplace transformation and perturbation technique,” Nonlinear Eng. Model. Appl., 7(4), 273-278, 2018.
R.Tripathi, H. K. Mishra, “Homotopy perturbation method with Laplace Transform (LT-HPM) for solving Lane–Emden type differential equations (LETDEs),” Springer Plus 5 (1), 1-21, 2016.
F. Yin, J. Song, F. Lu, H. Leng, “A coupled method of Laplace transform and Legendre wavelets for Lane-Emden-type differential equations,” J. Appl. Math., 2012, 1-16, 2012.
H. Eltayeb,“The combined Laplace transform and new homoyopy perturbation methods for Lane Emden type differential equations,” J. Nonlinear Analysis Appl., 2018 (2), 95-105, 2018.
T.M. Elzaki, “Solution of nonlinear differential equations using mixture of Elzaki transform and differential transform method,” Int. Math. Forum, 7(13), 631- 638, 2012.
E.Yusufoğlu, “Numerical solution of Duffing equation by the Laplace decomposition algorithm,” Appl.Math. Comput., 177 (2), 572–580, 2006.
A. N.Golshan, S. S. Nourazar, H. G.Fard, A.Yildirim, A. Campo, “A modified homotopy perturbation method coupled with the Fourier transform for nonlinear and singular Lane-Emden equations,” Appl. Math. Lett., 26 (10), 1018–1025, 2013.
A.Boggess, F. J. Narcowich, A first Course in Wavelets with Fourier Analysis, New Jersey: John Wiley & Sons 2015.ch.3.
L. C. Andrews, B. K. Shivamoggi,Integral Transforms for Engineering. Washington: SPIE Press, 1999, ch.2.
R. N. Bracewell,The Fourier Transform and Its Applications, Boston: McGraw- Hill, , 2000.ch.2
Osgood, Brad, The Fourier Transform and Its applications. Lecture notes for EE 261 (2009): 20
Wheeler, N. Simplified Production of Dirac Delta Function Identities. Reed College (1997)