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Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 1-2/2021

24.10.2020 | Original Research

Approximate solution of singular IVPs of Lane–Emden type and error estimation via advanced Adomian decomposition method

verfasst von: Umesh, Manoj Kumar

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2021

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Abstract

This article aims to present a simple and effective method, named as advanced Adomian decomposition method, to attain the approximate solution of singular initial value problems of Lane–Emden type. Also, convergence analysis and error analysis with an upper bound of the absolute error for the proposed method are discussed. The proposed method is capable to remove the singular behaviour of the problems and provides an approximate solution up to the desired order. To illustrate the reliability and validity of the proposed method with error estimate several examples that arise in applications are considered and the attained outcomes are compared with some existing numerical methods.
Vorheriger Artikel Approximation of fixed point and its application to fractional differential equation
Nächster Artikel Solving two generalized nonlinear matrix equations

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Literatur
1.
Lane, J.H.: On the theoretical temperature of the sun. Am. J. Sci. Arts 50, 57–74 (1870)CrossRef
2.
Emden, R.: Gaskugein: Anwendugen der mechanischen warmetheoric. B.G, Tewbner, Leipzig and Berlin (1907)
3.
Davis, H.T.: Introduction to Non-linear Differential and Integral Equations. Dover, New York (1962)
4.
Chandrasekhar, S.: Introduction to Study of Stellar Structure. Dover, New York (1967)
5.
Richardson, O.U.: The emission of electricity from hot bodies. Longman, Green and Co., London (1921)
6.
Chowdhury, M.S.H., Hashim, I.: Solutions of a class of singular second-order IVPs by homotopy-perturbation method. Phys. Lett. A 365, 439–447 (2007)MathSciNetMATHCrossRef
7.
Horedt, G.P.: Exact solutions of the Lane–Emden equation in N-dimensional space. Astron. Astrophys. 160, 148–156 (1986)MATH
8.
Horedt, G.P.: Approximate analytical solutions of the Lane–Emden equation in N-dimensional space. Astron. Astrophys. 172, 359–367 (1987)MathSciNetMATH
9.
10.
Alzate, P.P.C., Urueña, W.A.: The Zhou’s method for solving the White-Dwarfs equation. Appl. Math. 4, 28–32 (2013) CrossRef
11.
Khalique, C.M., Ntsime, P.: Exact solutions of the Lane–Emden type equations. New Astron. 13(7), 476–480 (2008)CrossRef
12.
Aminikhah, H., Moradian, S.: Numerical solution of singular Lane–Emden equation. ISRN Math. Phys. 2013, 1–9 (2013)MATHCrossRef
13.
Khan, Y., Svoboda, Z., Smarda, Z.: Solving certain classes of Lane–Emden type equations using the differential transformation method. Adv. Differ. Equ. 174, 1–11 (2012)MathSciNetMATH
14.
Yigider, M., Tabatabaei, K., Celik, E.: The numerical method for solving differential equations of Lane–Emden type by Pad’e approximation. Discrete Dyn. Nat. Soc. 2011, 1–9 (2011)MATHCrossRef
15.
Bhrawy, A.H., Alofi, A.S.: A Jacobi-Gauss collocation method for solving nonlinear Lane-Emden type equations. Commun. Nonlinear Sci. Numer. Simul. 17, 62–70 (2012)MathSciNetMATHCrossRef
16.
Singh, H.: An efficient computational method for the approximate solution of nonlinear Lane–Emden type equations arising in astrophysics. Astrophys. Space Sci. 363(4), 1–10 (2018)MathSciNetCrossRef
17.
Yin, F.K., Han, W.Y., Song, J.Q.: Modified Laplace decomposition method for Lane-Emden type differential equations. Int. J. Appl. Phys. Math. 3(2), 98–102 (2013)CrossRef
18.
Chowdhury, M.S.H., Hashim, I.: Solutions of Emden-Fowler equations by homotopy-perturbation method. Nonlinear Anal. Real World Appl. 10, 104–115 (2009)MathSciNetMATHCrossRef
19.
Parand, K., Shahini, M., Dehghan, M.: Rational Legendre pseudospectral approach for solving non-linear differential equations of Lane–Emden type. J. Comput. Phys. 228, 8830–8840 (2009)MathSciNetMATHCrossRef
20.
21.
Ramos, J.I.: Linearization techniques for singular initial-value problems of ordinary differential equations. Appl. Math. Comput. 161, 525–542 (2005)MathSciNetMATH
22.
Mandelzweig, V.B., Tabakin, F.: Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs. Comput. Phys. Commun. 141(2), 268–281 (2001)MathSciNetMATHCrossRef
23.
Duan, J.S., Rach, R., Wazwaz, A.M.: Higher-order numeric solutions of the Lane–Emden type equations derived from the multi-stage modified Adomian decomposition method. Int. J. Comput. Math. 94(1), 197–215 (2015)MathSciNetMATHCrossRef
24.
Aminikhah, H.: Solutions of the singular IVPs of Lane–Emden type equations by combining Laplace transformation and perturbation technique. Nonlinear Eng. 7(4), 273–278 (2018)MathSciNetCrossRef
25.
Bender, C.M., Milton, K.A., Pinsky, S.S., Simmons, J.L.M.: A new perturbative approach to non linear problems. J. Math. Phys. 30(7), 1447–1455 (1989)MathSciNetMATHCrossRef
26.
27.
28.
Duan, J.S.: Convenient analytic recurrence algorithms for the Adomian polynomials. Appl. Math. Comput. 217, 6337–6348 (2011)MathSciNetMATH
29.
30.
Kaliyappan, M., Hariharan, S.: Symbolic computation of Adomian polynomials based on Rach’s rule. Br. J. Math. Comput. Sci. 5(5), 562–570 (2015)CrossRef
31.
Liu, J.G., Yang, X.J., Feng, Y.Y.: On integrability of the time fractional nonlinear heat conduction equation. J. Geom. Phys. 144, 190–198 (2019)MathSciNetMATHCrossRef
32.
33.
Liu, J.G., Yang, X.J., Feng, Y.Y., Cui, P.: On group analysis of the time fractional extended (2+1)-dimensional Zakharov-Kuznetsov equation in quantum magneto-plasmas. Math. Comput. Simul. 178, 407–421 (2020)MathSciNetMATHCrossRef
34.
Feng, Y.Y., Yang, X.J., Liu, J.G.: On overall behavior of Maxwell mechanical model by the combined Caputo fractional derivative. Chin. J. Phys. 66, 269–276 (2020)MathSciNetCrossRef
35.
Cherruault, Y., Adomian, G.: Decomposition methods: a new proof of convergence. Comput. Math. Appl. 18(12), 103–106 (1993)MathSciNetMATH
36.
Abdelrazec, A., Pelinovsky, D.: Convergence of the Adomian decomposition method for initial-value problems. Numer. Methods Partial Differ. Equ. 27(4), 749–766 (2009)MathSciNetMATHCrossRef
37.
38.
Ray, S.S.: New approach for general convergence of the Adomian decomposition method. World Appl. Sci. J. 32(11), 2264–2268 (2014)
39.
40.
Warne, P.G., Polignone, W.D.A., Sochacki, J.S., Parker, G.E., Carothers, D.C.: Explicit A—priori error bounds and Adaptive error control for approximation of non-linear initial value differential systems. Comput. Math. Appl. 52, 1695–1710 (2006)MathSciNetMATHCrossRef
41.
Yuzbasi, S.: A numerical approach for solving a class of the nonlinear Lane–Emden type equations arising in astrophysics. Math. Methods Appl. Sci. 34, 2218–2230 (2011)MathSciNetMATHCrossRef
42.
Wazwaz, A.M.: A new algorithm for solving differential equations of Lane–Emden type. Appl. Math. Comput. 118, 287–310 (2001)MathSciNetMATH
43.
Doha, E.H., Bhrawy, A.H., Hafez, R.M., Gorder, R.A.: A Jacobi rational pseudospectral method for Lane–Emden initial value problems arising in astrophysics on a semi-infinite interval. Comput. Appl. Math. 33, 607–619 (2014)MathSciNetMATHCrossRef
44.
Mall, S., Chakraverty, S.: Chebyshev neural network based model for solving Lane–Emden type equations. Appl. Math. Comput. 247, 100–114 (2014)MathSciNetMATH
45.
Pandey, R.K., Kumar, N.: Solution of Lane–Emden type equations using Bernstein operational matrix of differentiation. New Astron. 17(3), 303–308 (2012)CrossRef
Metadaten
Titel
Approximate solution of singular IVPs of Lane–Emden type and error estimation via advanced Adomian decomposition method
verfasst von
Umesh
Manoj Kumar
Publikationsdatum
24.10.2020
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2021
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-020-01444-2

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