Numerical study of astrophysics equations using Bessel collocation methods of first Kind

Arora, Shelly; Bala, Indu

doi:10.22034/cmde.2024.52330.2333

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

تعداد نشریات	45
تعداد شماره‌ها	1,419
تعداد مقالات	17,506
تعداد مشاهده مقاله	56,598,782
تعداد دریافت فایل اصل مقاله	18,782,200

	Numerical study of astrophysics equations using Bessel collocation methods of first Kind
Computational Methods for Differential Equations
مقاله 8، دوره 13، شماره 2، خرداد 2025، صفحه 466-478 اصل مقاله (419.58 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.52330.2333
نویسندگان
Shelly Arora؛ Indu Bala^*
Department of Mathematics‎, ‎Punjabi University‎, ‎Patiala‎, ‎147002‎, ‎Punjab‎, ‎India.
چکیده
A hybrid computational procedure of Newton Raphson method and orthogonal collocation method have been applied to study the behavior of nonlinear astrophysics equations. The nonlinear Lane Emden equation has been discretized using the orthogonal collocation method using $n^{th}$-order Bessel polynomial as $J_n(\xi)$ as base function. The system of collocation equations has been solved numerically using Newton Raphson method. Numerical examples have been discussed to check the reliability and efficiency of the scheme. Numerically calculated results have been compared to the exact values as well as the values already given in the literature to check the compatibility of the scheme. Error analysis has been studied by calculating the absolute error, $L_2- norm$ and $L_{\infty}- norm$. Computer codes have been prepared using MATLAB.
کلیدواژه‌ها
Astrophysics equations؛ Orthogonal collocation؛ Newton Rephson method؛ Polytropic fluid

مراجع
[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.
آمار تعداد مشاهده مقاله: 242 تعداد دریافت فایل اصل مقاله: 486

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Numerical study of astrophysics equations using Bessel collocation methods of first Kind