Affiliation:
1. Department of Applied Mathematics and Humanities , S. V. National Institute of Technology Surat , Surat 395007 , Gujarat , India
Abstract
Abstract
This paper suggests the Chebyshev pseudo-spectral approach to solve the variable-order fractional Lane–Emden differential equations (VOFLEDE). The variable-order fractional derivative (VOFD) is defined in the Caputo sense. The proposed method transforms the problem into a set of algebraic equations that can be solved for unknowns. Few examples are discussed to exhibit the viability and effectiveness of the approach. The present study indicates the accuracy, efficiency, and powerfulness of the Chebyshev collocation method in solving the VOFD Lane–Emden equation. Error bound and convergence analysis of the method is also discussed. It is worth noticing that using lesser collocation nodes in computation is another advantage of the technique, which eventually reduces the computational cost.
Subject
Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics
Reference48 articles.
1. R. P. Agarwal and D. O’Regan, “Existence theory for single and multiple solutions to singular positone boundary value problems,” J. Differ. Equ., vol. 175, no. 2, pp. 393–414, 2001. https://doi.org/10.1006/jdeq.2001.3975.
2. R. P. Agarwal, D. O’Regan, and B. Yan, “Positive solutions for singular three-point boundary-value problems,” Electron. J. Differ. Equ., vol. 2008, no. 116, pp. 1–20, 2008.
3. V. K. Baranwal, R. K. Pandey, M. P. Tripathi, and O. P. Singh, “An analytic algorithm of Lane-Emden-type equations arising in astrophysics-a hybrid approach,” J. Theor. Appl. Phys., vol. 6, no. 1, p. 22, 2012. https://doi.org/10.1186/2251-7235-6-22.
4. A. Boucherif, “Positive solutions of second-order boundary value problems,” Differ. Differ., vol. 2006, p. 231, 2006.
5. S. Chandrasekhar and S. Chandrasekhar, An Introduction to the Study of Stellar Structure, vol. 2, Chicago, Courier Corporation, 1957.
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