Infinite Taylor Series Method for Solving Lane-Emden Type Equations

Year 2020, Volume: 17 Issue: 1, 1 - 10, 01.05.2020

Morufu Oyedunsi Olayiwola Adebisi Adegoke

Abstract

In this research article, a numerical approach to the solutions of different forms of Lane-Emden type of singular initial value problems is presented, The Taylor Series Method has been applied. Application was on singular initial value problems. Comparison with exact solution shows considerable acceleration in convergence. The method is effective and easy to implement.

Keywords

Lane-Emden, Taylor Series, Singular Initial Value Problem

References

• [1] C. K. Chen, S. S. Chen, Application of the differential transformation method to anon-linear conservative system, Applied Mathematics and Computation, 154, (2004), 431-441.
• [2] T. M. A. El-Mistikawy, Comment on the three-dimensional flow past a stretching sheet and the Homotopy perturbation method, Computers & Mathematics with Applications, 57(3), (2009), 404-406.
• [3] J. H. He, Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178, (1999), 257-262.
• [4] J. H. He, Homotopy Perturbation technique. Computer Methods in Applied Mechanics and Engineering, 178, (1999), 257-262.
• [5] J. H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non-Linear Mechanics, 35, (2000), 37-43.
• [6] J. H. He, A coupling method Homotopy perturbation technique and a perturbation technique for nonlinear problems, International Journal of Non-Linear Mechanics, 35, (2003), 73-79.
• [7] Jos´e Juan Rodrıguez Cano, Enrique de Amo, Taylor’s Expansion Revisited.A General Formula for the Remainder, Hindawi Publishing Corporation, International Journal of Mathematics and Mathematical Sciences, 2012, (2012), Article ID 645736.
• [8] H. K. Mishra, A. K. Nagar, He-Laplace method for linear and nonlinear partial differential equations, Journal of Applied Mathematics, (2012), 1-16.
• [9] H. K. Mishra, He-Laplace Method for the solution of two-point boundary value problems, American Journal of Mathematical Analysis, 2(3), (2014), 45-49.
• [10] E. Momoniat, C. Harley, Approximate implicit solution of a Lane-Emden equation. New Aston, (2006), 520-526.
• [11] M. O. Olayiwola. Solutions of Emden-Fowler type equation by viterational iteration method, Cankaya University Journal of Science and Engineering, 16(2), (2019), 001-009.
• [12] J. I. Ramos, Series Approach to the Lane-Emden equation and comparison with the Homotopy perturbation method, Chaos Solitons Fractals, 38(2), (2008), 400-408.
• [13] N. Tsirivas, A generalization of universal Taylor series in simply connected domains, Journal of Mathematical Analysis and Applications, 388, (2012), 361-369.
• [14] Yahya Qaid Hasan, Liu Ming Zhu, Solving singular initial problems in the second-order Ordinary Differential Equations. Journal of Applied Science, 7(17), (2007), 2505-2508.