A coupled method of laplace transform and legendre wavelets for Lane-Emden-type differential equations

Journal of Applied Mathematics

Volumn 2012, Issue , 2012, Pages

  Yin, Fukang ^a   Song, Junqiang ^a   Lu, Fengshun ^b   Leng, Hongze ^a  

^a NATIONAL UNIVERSITY OF DEFENSE TECHNOLOGY   (China)

^b CHINA AERODYNAMICS RESEARCH AND DEVELOPMENT CENTER   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84871364119     PISSN: 1110757X     EISSN: 16870042     Source Type: Journal    
DOI: 10.1155/2012/163821     Document Type: Article

References (38)

1. Chandrasekhar S., An Introduction to the Study of Stellar Structure 1967 New York, NY, USA Dover 0092663 ZBL0123.23604
2. Davis H. T., Introduction to Nonlinear Differential and Integral Equations 1962 New York, NY, USA Dover 0181773 ZBL0217.54002
3. Richardson O. U., The Emission of Electricity From Hot Bodies 1921 London, UK Zongmans Green and Company
4. Shawagfeh N. T., Nonperturbative approximate solution for Lane-Emden equation. Journal of Mathematical Physics 1993 34 9 4364 4369 10.1063/1.530005 1233277 ZBL0780.34007
5. Wazwaz A.-M., A new algorithm for solving differential equations of Lane-Emden type. Applied Mathematics and Computation 2001 118 2-3 287 310 10.1016/S0096-3003(99)00223-4 1812960 ZBL1023.65067 (Pubitemid 33592922)
6. Wazwaz A.-M., A new method for solving singular initial value problems in the second-order ordinary differential equations. Applied Mathematics and Computation 2002 128 1 45 57 10.1016/S0096-3003(01)00021-2 1891179 ZBL1030.34004 (Pubitemid 34182422)
7. Olga F., Zdeněk Š., A domian decomposition method for certain singular initial value problems. Journal of Applied Mathematics 2010 3 2 91 98
8. Ramos J. I., Series approach to the Lane-Emden equation and comparison with the homotopy perturbation method. Chaos, Solitons and Fractals 2008 38 2 400 408 10.1016/j.chaos.2006.11.018 2415942 ZBL1146.34300 (Pubitemid 351627012)
9. Yildirim A., Öziş T., Solutions of singular IVP's of Lane-Emden type by homotopy pertutbation method. Physics Letters A 2007 369 70 76
10. Chowdhury M. S. H., Hashim I., Solutions of a class of singular second-order IVPs by homotopy-perturbation method. Physics Letters A 2007 365 5-6 439 447 10.1016/j.physleta.2007.02.002 2308783 ZBL1203.65124
11. He J.-H., Variational approach to the Lane-Emden equation. Applied Mathematics and Computation 2003 143 2-3 539 541 10.1016/S0096-3003(02)00382-X 1981715 ZBL1022.65076
12. Dehghan M., Shakeri F., Approximate solution of a differential equation arising in astrophysics using the variational iteration method. New Astronomy 2008 13 1 53 59 2-s2.0-34548509029 10.1016/j.newast.2007.06.012 (Pubitemid 47371215)
13. Yildirim A., Öziş T., Solutions of singular IVPs of Lane-Emden type by the variational iteration method. Nonlinear Analysis 2009 70 6 2480 2484 10.1016/j.na.2008.03.012 2498349 ZBL1162.34005
14. Liao S., A new analytic algorithm of Lane-Emden type equations. Applied Mathematics and Computation 2003 142 1 1 16 10.1016/S0096-3003(02)00943-8 1978243 ZBL1022.65078
15. Bataineh A. S., Noorani M. S. M., Hashim I., Homotopy analysis method for singular IVPs of Emden-Fowler type. Communications in Nonlinear Science and Numerical Simulation 2009 14 4 1121 1131 10.1016/j.cnsns.2008.02.004 2468944 ZBL1221.65197
16. Mohan C., Al-Bayaty A. R., Power-series solutions of the Lane-Emden equation. Astrophysics and Space Science 1980 73 1 227 239 10.1007/BF00642378 596868 ZBL0457.76039
17. Ertürk V. S., Differential transformation method for solving differential equations of Lane-Emden type. Mathematical & Computational Applications 2007 12 3 135 139 2396843 ZBL1175.34007 (Pubitemid 351280296)
18. Mukherjee S., Roy B., Chaterjee P. K., Solution of Lane-Emden equation by differential transform method. International Journal of Nonlinear Science 2011 12 4 478 484 2875902
19. Parand K., Razzaghi M., Rational legendre approximation for solving some physical problems on semi-infinite intervals. Physica Scripta 2004 69 5 353 357 2-s2.0-2442639373 10.1238/Physica.Regular.069a00353
20. Parand K., Pirkhedri A., Sinc-Collocation method for solving astrophysics equations. New Astronomy 2010 15 6 533 537 2-s2.0-77950338358 10.1016/j.newast.2010.01.001
21. Parand K., Rezaei A. R., Taghavi A., Lagrangian method for solving Lane-Emden type equation arising in astrophysics on semi-infinite domains. Acta Astronautica 2010 67 7-8 673 680 2-s2.0-78049432455 10.1016/j.actaastro.2010.05. 015
22. Motsa S. S., Sibanda P., A new algorithm for solving singular IVPs of Lane-Emden type. Proceedings of the 4th International Conference on Applied Mathematics, Simulation, Modelling (ASM '10) July 2010 Corfu Island, Greece NAUN International Conferences 176 180
23. Karimi Vanani S., Aminataei A., On the numerical solution of differential equations of Lane-Emden type. Computers & Mathematics with Applications 2010 59 8 2815 2820 10.1016/j.camwa.2010.01.052 2607987 ZBL1193.65151
24. Yang C., Hou J., A numerical method for Lane-Emden equations using hybrid functions and the collocation method. Journal of Applied Mathematics 2012 2012 9 316534 10.1155/2012/316534 2880829 ZBL1235.65107
25. Yousefi S. A., Legendre wavelets method for solving differential equations of Lane-Emden type. Applied Mathematics and Computation 2006 181 2 1417 1422 10.1016/j.amc.2006.02.031 2270772 ZBL1105.65080 (Pubitemid 44646613)
26. Pandey R. K., Kumar N., Bhardwaj A., Dutta G., Solution of Lane-Emden type equations using legendre operational matrix of differentiation. Applied Mathematics and Computation 2012 218 14 7629 7637 10.1016/j.amc.2012.01.032 2892729 ZBL1246.65115
27. Boyd J. P., Chebyshev spectral methods and the Lane-Emden problem. Numerical Mathematics 2011 4 2 142 157 2862664
28. Khuri S. A., A Laplace decomposition algorithm applied to a class of nonlinear differential equations. Journal of Applied Mathematics 2001 1 4 141 155 10.1155/S1110757X01000183 1884973 ZBL0996.65068
29. Khan Y., An effective modification of the laplace decomposition method for nonlinear equations. International Journal of Nonlinear Sciences and Numerical Simulation 2009 10 11-12 1373 1376
30. Khan M., Gondal M. A., A new analytical solution of foam drainage equation by laplace decomposition method. Journal of Advanced Research in Scientific Computing 2010 2 2 53 64 2792623
31. Abbasbandy S., Application of He's homotopy perturbation method for Laplace transform. Chaos, Solitons and Fractals 2006 30 5 1206 1212 2-s2.0-33745835072 10.1016/j.chaos.2005.08.178 (Pubitemid 44037391)
32. Khuri S. A., Sayfy A., A laplace variational iteration strategy for the solution of differential equations. Applied Mathematics Letters 2012 25 12 2298 2305 2-s2.0-84865482047 10.1016/j.aml.2012.06.020
33. Madani M., Fathizadeh M., Homotopy perturbation algorithm using laplace transformation. Nonlinear Science Letters A 2010 1 263 267
34. Khan M., Gondal M. A., Karimi Vanani S., On the coupling of homotopy perturbation and laplace transformation for system of partial differential equations. Applied Mathematical Sciences 2012 6 9-12 467 478 2879393 ZBL1247.65136
35. Madani M., Fathizadeh M., Khan Y., Yildirim A., On the coupling of the homotopy perturbation method and laplace transformation. Mathematical and Computer Modelling 2011 53 9-10 1937 1945 10.1016/j.mcm.2011.01.023 2782897 ZBL1219.65121
36. Khan Y., Wu Q., Homotopy perturbation transform method for nonlinear equations using He's polynomials. Computers & Mathematics with Applications 2011 61 8 1963 1967 10.1016/j.camwa.2010.08.022 2785523 ZBL1219.65119
37. Gupta V. G., Gupta S., Homotopy perturbation transform method for solving initial boundary value problems of variable coefficients. International Journal of Nonlinear Science 2011 12 3 270 277 2862359
38. Singh J., Kumar D., Rathore S., Application of homotopy perturbation transform method for solving linear and nonlinear Klein-Gordon equations. Journal of Information and Computing Science 2012 7 131 139