Modified Differential Transform Method for Singular Lane-Emden Equations in Integer and Fractional Order
Yıl 2015,
Cilt: 5 Sayı: 1, 124 - 131, 01.06.2015
H. R. Marasi
N. Sharifi
H. Piri
Öz
In the present work the modiŞed differential transform method, incorporating the Adomian polynomials into the differential transform method DTM , is used tosolve the nonlinear and singular Lane-Emden equations in integer and fractional order.Numerical examples with different types are solved. The results show that this methodis very effective and simple
Kaynakça
- Agarwal, R. P., Regan, D. O. and Lakshmikanthamr, V., (2001), Quadratic forms and nonlinear non- resonant singular second order boundary value problems of limit circle type, Zeitschrift fur Analysis und ihre Anwendungen, 20, pp. 727-737.
- Agarwal, R. P. and Regan, D. O., (2001), Existence theory for single and multiple solutions to singular positone boundary value problems, J. Diff. Equ., 175(2), pp. 393-414.
- Lane, J. H., (1870), On the theoretical temperature of the sun under the hypothesis of a gaseous mass maintaining its volume by its internal heat and depending on the laws of gases known to terrestrial experiment, The American Journal of Science and Arts, 50, pp. 57-74.
- Emden, R., (1907), Gaskugeln, Teubner, Leipzig and Berlin.
- Marasi, H. R. and Nikbakht, M., (2011), Adomian decompositiom method for boundary value prob- lems, Aus. J. Basic. Appl. Sci., 5, pp. 2106-2111.
- Adomian, G., (1994), Solving frontier problems of physics: The decomposition method, Kluwer Aca- demic, Dordrecht.
- Marasi, H.R. and Karimi, S., (2014), Convergence of variational iteration method for solving fractional Klein-Gordon equation, J. Math. Comp. Sci., 4, pp. 257-266.
- Assas, L. M. B., (2008), Variational iteration method for solving coupled-KdV equations, Chaos Solitons Fractals., 38(4), pp. 1225-1228.
- Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., (2006), Theory and applications of fractional differential equations, North-Holland Mathematics Studies., 204, pp. 7-10.
- Podlubny, I., (1999), Fractional differential equations, Academic Press, New york.
- Marasi, H. R. and Jodayree Akbarfam, A., (2007), On the canonical solution of indeŞnite problem with m turning points of even order, J. Math. Anal. Appl., 332, pp. 1071-1086
- Marasi, H. R., (2011), Asymptotic form and inŞnite product representation of solution of a second order initial value problem with a complex parameter and a Şnite number of turning points, J. Cont. Math. Anal., 4, pp. 57-76
- Marasi, H. R. and Jodayree Akbarfam, A., (2012), Dual equation and inverse problem for an indefnite Sturm-Liouville problem with m turning points of even order, Math. Modell. Anal., 17(5), pp. 618-629. [14] Chowdhury, M. and Hashim, I., (2009), Solutions of Emden-Fowler equations by homotopy perturba- tion method, Non-Linear Analysis: Real World Application., 101, pp. 104-115.
- Yildirim, A. and Ozi, T., (2009), Solutions of singular IVPs of Lane-Emden type by the variational iteration method, Nonlinear Analysis: Theory, Methods Applications, 70(6), pp. 2480-2484.
- Parand, K. and Pirkhedri, A., (2010), Sinc-collocation method for solving astrophysics equations, New Astronomy, 15(6), pp. 533-537.
- He, J., (2006), Homotopy perturbation method for solving boundary value problems, Phys. Lett. A., 350, pp. 87-88.
- Zhou, J. K., (1986), Deferential transformation and its application for electrical circuits, Huazhong University Press, Wuhan China.
- Nazari-Golshan, A., Nourazar, S. S., Ghafoori-Fard, H., Yildirim, A. and Campo, A., (2013), A modiŞed homotopy perturbation method coupled with the Fourier transform for nonlinear and singular Lane-Emden equations, Appl. Math. Lett., http://dx.doi.org/10.1016/j.aml., pp. 2013.05.010.
- Elsaid, A., (2012), Fractional differential transform method combined with the Adomian polynomials, Apll. Math. Comput., 218, pp. 6899-6911.
Yıl 2015,
Cilt: 5 Sayı: 1, 124 - 131, 01.06.2015
H. R. Marasi
N. Sharifi
H. Piri
Kaynakça
- Agarwal, R. P., Regan, D. O. and Lakshmikanthamr, V., (2001), Quadratic forms and nonlinear non- resonant singular second order boundary value problems of limit circle type, Zeitschrift fur Analysis und ihre Anwendungen, 20, pp. 727-737.
- Agarwal, R. P. and Regan, D. O., (2001), Existence theory for single and multiple solutions to singular positone boundary value problems, J. Diff. Equ., 175(2), pp. 393-414.
- Lane, J. H., (1870), On the theoretical temperature of the sun under the hypothesis of a gaseous mass maintaining its volume by its internal heat and depending on the laws of gases known to terrestrial experiment, The American Journal of Science and Arts, 50, pp. 57-74.
- Emden, R., (1907), Gaskugeln, Teubner, Leipzig and Berlin.
- Marasi, H. R. and Nikbakht, M., (2011), Adomian decompositiom method for boundary value prob- lems, Aus. J. Basic. Appl. Sci., 5, pp. 2106-2111.
- Adomian, G., (1994), Solving frontier problems of physics: The decomposition method, Kluwer Aca- demic, Dordrecht.
- Marasi, H.R. and Karimi, S., (2014), Convergence of variational iteration method for solving fractional Klein-Gordon equation, J. Math. Comp. Sci., 4, pp. 257-266.
- Assas, L. M. B., (2008), Variational iteration method for solving coupled-KdV equations, Chaos Solitons Fractals., 38(4), pp. 1225-1228.
- Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J., (2006), Theory and applications of fractional differential equations, North-Holland Mathematics Studies., 204, pp. 7-10.
- Podlubny, I., (1999), Fractional differential equations, Academic Press, New york.
- Marasi, H. R. and Jodayree Akbarfam, A., (2007), On the canonical solution of indeŞnite problem with m turning points of even order, J. Math. Anal. Appl., 332, pp. 1071-1086
- Marasi, H. R., (2011), Asymptotic form and inŞnite product representation of solution of a second order initial value problem with a complex parameter and a Şnite number of turning points, J. Cont. Math. Anal., 4, pp. 57-76
- Marasi, H. R. and Jodayree Akbarfam, A., (2012), Dual equation and inverse problem for an indefnite Sturm-Liouville problem with m turning points of even order, Math. Modell. Anal., 17(5), pp. 618-629. [14] Chowdhury, M. and Hashim, I., (2009), Solutions of Emden-Fowler equations by homotopy perturba- tion method, Non-Linear Analysis: Real World Application., 101, pp. 104-115.
- Yildirim, A. and Ozi, T., (2009), Solutions of singular IVPs of Lane-Emden type by the variational iteration method, Nonlinear Analysis: Theory, Methods Applications, 70(6), pp. 2480-2484.
- Parand, K. and Pirkhedri, A., (2010), Sinc-collocation method for solving astrophysics equations, New Astronomy, 15(6), pp. 533-537.
- He, J., (2006), Homotopy perturbation method for solving boundary value problems, Phys. Lett. A., 350, pp. 87-88.
- Zhou, J. K., (1986), Deferential transformation and its application for electrical circuits, Huazhong University Press, Wuhan China.
- Nazari-Golshan, A., Nourazar, S. S., Ghafoori-Fard, H., Yildirim, A. and Campo, A., (2013), A modiŞed homotopy perturbation method coupled with the Fourier transform for nonlinear and singular Lane-Emden equations, Appl. Math. Lett., http://dx.doi.org/10.1016/j.aml., pp. 2013.05.010.
- Elsaid, A., (2012), Fractional differential transform method combined with the Adomian polynomials, Apll. Math. Comput., 218, pp. 6899-6911.