Research Article
Year 2022,
Volume: 17 Issue: 2, 247 - 260, 25.11.2022
Abstract
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.
References
- 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)
Year 2022,
Volume: 17 Issue: 2, 247 - 260, 25.11.2022
Abstract
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.
References
- 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)
There are 20 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | November 25, 2022 |
| Published in Issue | Year 2022 Volume: 17 Issue: 2 |
