- [1] S. Arora, S. S Dhaliwal, and V. K. Kukreja, Solution of two point boundary value problems using orthogonal collocation on finite elements, Appl. Math. Comput., 171 (2005), 358–370.
- [2] S. Arora and I. Kaur, Applications of Quintic Hermite collocation with time discretization to singularly perturbed problems. Appl. Math. Comput, 316 (2018) 409-421.
- [3] W. N. Bailey, Generalized Hypergeometric Series, Hafner, New York, 1972.
- [4] A. H. Bhrawy and A. S. Alofi, A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equation, Commun. Nonlinear Sci., 17 (2012), 62–70.
- [5] J. P. Boyd, Chebyshev spectral methods and the Lane-Emden problem, Numer. Math. Theor. Method. Appl., 4 (2011), 142–157.
- [6] N. Caglar and H. Caglar, B-spline solution of singular boundary value problems, Appl. Math. Comput., 182 (2006), 1509-1513.
- [7] S. Chandrasekhar, An Introduction to the Study of Stellar Structure, Dover, New York , 1967.
- [8] W. D. Evans, W. N. Everitt, K. H. Kwon, and L. L. Littlejohn, Real orthogonalizing weights for Bessel polynomials, J. Comput. Appl. Math., 49 (1993), 51–57.
- [9] W. N. Everitt and C. Markett, On a generalization of Bessel functions satisfying higher-order differential equations, J. Comput. Appl. Math., 54 (1994), 325-349.
- [10] B. A. Finlayson, Packed bed reactor analysis by orthogonal collocation, Chem. Eng. Sci., 26 (1971), 1081–1091.
- [11] N. B. Ferguson and B. A. Finlayson, Transient chemical reaction analysis by orthogonal collocation, Chem. Eng J., 1(4) (1970), 327–336.
- [12] W. Gautschi, Numerical Analysis, Second Edition, Springer-Verlag, New York, (2012).
- [13] S. Gümgüm, Taylor wavelet solution of linear and nonlinear Lane-Emden equations, Appl. Numer. Math., 158(2020), 44–53.
- [14] A. Karimi Dizicheh, S. Salahshour, A. Ahmadian, and D. Baleanu, A novel algorithm based on the Legendre wavelets spectral technique for solving the LaneEmden equations, Appl. Numer. Math., 153 (2020), 443–456.
- [15] T. H. Koornwinder, Orthogonal polynomial with weight function (1−x)α(1−x)β +Mδ(x−1)+Nδ(x−1), Can. Math. Bull., 27(2) (1984), 205–214.
- [16] H. MacMullen, J. J. H. Miller, E. ORiordana, and G. I. Shishkinc, A second-order parameter-uniform overlapping Schwarz method for reactiondiffusion problems with boundary layers, J. Comput. Appl. Math., 130 (2001), 231244.
- [17] N. W. McLACHLAN, Bessel functions for engineers, Second Edition, Oxford University Press, 1961.
- [18] J. J. H. Miller, E. ORiordan, and G. I. Shishkin, Fitted numerical methods for singular perturbation problems, error estimate in the maximum norm for linear problems in one and two dimensions. World Scientific, United States, 2012.
- [19] P. Mishra, K. K. Sharma, A. K. Pani, and G. Fairweather, Orthogonal spline collocation for singularly perturbed reaction diffusin problems in one dimention. Int. J. Numer. Anal. Mod., 16 (2019), 647-667.
- [20] M. A. Noor and M. Waseem, Some iterative method for solving a system of nonlinear equations, Comput. Math. Appl., 57 (2009), 101–106.
- [21] K. Paranda and M. Hemamia, Numerical study of astrophysics equations by meshless collocation method based on compactly supported radial basis function, Int. J. Comput. Math., 3 (2017), 1053–1075.
- [22] P. M. Prenter, Splines and variational methods, Wiley interscience publication, 1975.
- [23] E. D. Rainville, Special functions, The Macmillan Company, New York, 1971.
- [24] S. L. Ross, Differential Equations Third Eddition, Uniersity of New Hampshire, 1984.
- [25] I. N. Sneddon, Special function of mathematical physics and chemistry, Third Eddition, Longman Mathematical Texts, 1980.
- [26] Swati, M. Singh, and K. Singh, An efficient technique based on higher order Haar wavelet method for LaneEmden equations, Math. Comput. Simul., 206(2023), 21–39.
- [27] J. V. Villadsen and W. E. Stewart, Solution of boundary value problem by orthogonal collocation, Chem. Eng. Sci., 22 (1967), 1483–1501.
- [28] G. N. Watson, The Theory of Bessel Functions, Cambridge University Press, Cambridge, 1994.
- [29] Ş. Yüzbaş, A numerical approximation based on the Bessel functions of first kind for solutions of Riccati type differential-difference equations, Comput. Math. Appl., 64(6) (2012), 1691–1705.
- [30] Ş. Yüzbaş, An improved Bessel collocation method with a residual error function to solve a class of LaneEmden differential equations, Math. Comput. Modelling, 57 (2013), 1298–1311.
- [31] Ş. Yüzbaş, Bessel collocation approach for solving continuous population models for single and interacting species, Appl. Math. Model, 36 (2012), 3787-3802.
- [32] Ş. Yüzbaş, and M. Sezer, An improved Bessel collocation method with a residual error function to solve a class of LaneEmden differential equations, Math. Comput. Model., 57 (2013), 1298-1311.
|