An improved Bessel collocation method with a residual error function to solve a class of Lane-Emden differential equations

Mathematical and Computer Modelling

Volumn 57, Issue 5-6, 2013, Pages 1298-1311

  YüzbaşI, Şuayip ^a   Sezer, Mehmet ^b  

^a MUGLA SITKI KOCMAN UNIVERSITY   (Turkey)

^b CELAL BAYAR UNIVERSITY   (Turkey)

Author keywords

Approximation solution; Bessel collocation method; Bessel functions of the first kind; Lane Emden differential equations; Modified Bessel collocation method

Indexed keywords

ABSOLUTE ERROR; APPROXIMATE SOLUTION; APPROXIMATION SOLUTION; BESSEL COLLOCATION METHODS; BESSEL FUNCTIONS OF THE FIRST KIND; BESSEL POLYNOMIALS; ERROR PROBLEMS; EXACT SOLUTION; RESIDUAL ERROR;

DIFFERENTIAL EQUATIONS;

BESSEL FUNCTIONS;

EID: 84873077054     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2012.10.032     Document Type: Article

References (31)

1. Chambre P.L. On the solution of the Poisson-Boltzmann equation with application to the theory of thermal explosions. J. Chem. Phys. 1952, 20:1795-1797.
2. Chandrasekhar S. Introduction to the Study of Stellar Structure 1967, Dover, New York.
3. Richardson O.U. The Emission of Electricity from Hot Bodies 1921, Longman, Green and Co., London, New York.
4. Yildirim A., Öziş T. Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method. Phys. Lett. A 2007, 369:70-76.
5. Ramos J.I. Series approach to the Lane-Emden equation and comparison with the homotopy perturbation method. Chaos Soliton Fractals 2008, 38:400-408.
6. Chowdhury M.S.H., Hashim I. Solutions of Emden-Fowler equations by homotopy-perturbation method. Nonlinear Anal. RWA 2009, 10:104-115.
7. Yousefi S.A. Legendre wavelets method for solving differential equations of Lane-Emden type. Appl. Math. Comput. 2006, 181:1417-1422.
8. Yildirim A., Öziş T. Solutions of singular IVPs of Lane-Emden type by the variational iteration method. Nonlinear Anal. 2009, 70:2480-2484.
9. Dehghan M., Shakeri F. Approximate solution of a differential equation arising in astrophysics using the variational iteration method. New Astron. 2008, 13:53-59.
10. Caglar N., Caglar H. B-spline solution of singular boundary value problems. Appl. Math. Comput. 2006, 182:1509-1513.
11. Wazwaz A.M. A new algorithm for solving differential equations of Lane-Emden type. Appl. Math. Comput. 2001, 118:287-310.
12. YüzbaşI Ş., Sezer M. A collocation approach to solve a class of Lane-Emden type equations. J. Adv. Res. Appl. Math. 2011, 3(2):58-73.
13. Vanani S.K., Aminataei A. On the numerical solution of differential equations of Lane-Emden type. Comput. Math. Appl. 2010, 59:2815-2820.
14. Parand K., Shahini A., Dehghan M. Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type. J. Comput. Phys. 2009, 228:8830-8840.
15. Shawagfeh N.T. Nonperturbative approximate solution for Lane-Emden equation. J. Math. Phys. 1993, 34(9):43-64.
16. Parand K., Dehghan Mehdi, Rezaei A.R., Ghaderi S.M. An approximation algorithm for the solution of the nonlinear Lane-Emden type equations arising in astrophysics using Hermite functions collocation method. Comput. Phys. Comm. 2010, 181:1096-1108.
17. He Ji-Huan Variational approach to the Lane-Emden equation. Appl. Math. Comput. 2003, 143:539-541.
18. YüzbaşI Ş., Şahin N., Sezer M. A Bessel polynomial approach for solving linear neutral delay differential equations with variable coefficients. J. Adv. Res. Differ. Equ. 2011, 3(1):81-101.
19. YüzbaşI Ş., Şahin N. Numerical solution of a class of Lane-Emden type differential-difference equations. J. Adv. Res. Sci. Comput. 2011, 3(3):14-29.
20. YüzbaşI Ş., Şahin N., Sezer M. Numerical solutions of systems of linear Fredholm integro-differential equations with Bessel polynomial bases. Comput. Math. Appl. 2011, 61(10):3079-3096.
21. YüzbaşI Ş. A numerical approach for solving the high-order linear singular differential-difference equations. Comput. Math. Appl. 2011, 62(5):2289-2303.
22. YüzbaşI Ş., Şahin N., Sezer M. Bessel matrix method for solving high-order linear Fredholm integro-differential equations. J. Adv. Res. Appl. Math. 2011, 3(2):23-47.
23. Şahin N., YüzbaşI Ş., Gülsu M. A collocation approach for solving systems of linear Volterra integral equations with variable coefficients. Comput. Math. Appl. 2011, 62:755-769.
24. YüzbaşI Ş., Şahin N., Sezer M. A Bessel collocation method for numerical solution of generalized pantograph equations. Numer. Methods Partial Differential Equations 2012, 28(4):1105-1123.
25. Oliveira F.A. Collocation and residual correction. Numer. Math. 1980, 36:27-31.
26. Çelik I. Approximate calculation of eigenvalues with the method of weighted residuals-collocation method. Appl. Math. Comput. 2005, 160:401-410.
27. Shahmorad S. Numerical solution of the general form linear Fredholm-Volterra integro-differential equations by the Tau method with an error estimation. Appl. Math. Comput. 2005, 167:1418-1429.
28. Çelik I. Collocation method and residual correction using Chebyshev series. Appl. Math. Comput. 2006, 174:910-920.
29. Gulsu M., Sezer M. A Taylor polynomial approach for solving differential-difference equations. J. Comput. Appl. Math. 2006, 186:349-364.
30. YalçInbaş S., Sezer M., Sorkun H.H. Legendre polynomial solutions of high-order linear Fredholm integro-differential equations. Appl. Math. Comput. 2009, 210:334-349.
31. Akyüz-DaşcIoǧlu A., Sezer M. Chebyshev polynomial solutions of systems of higher-order linear Fredholm-Volterra integro-differential equations. J. Franklin Inst. 2005, 342:688-701.