Journal
CHAOS SOLITONS & FRACTALS
Volume 103, Issue -, Pages 131-138Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2017.05.042
Keywords
Fractional vibration equation; Legendre scaling functions; Operational matrices; Error analysis; Convergence analysis
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Funding
- Department of Atomic Energy, National Institute of Science Education and Research (NISER), Odisha, India
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The key purpose of this article is to introduce a numerical algorithm for the solution of the fractional vibration equation (FVE). The numerical algorithm is based on the applications of the operational matrices of the Legendre scaling functions. The main advantage of the numerical algorithm is that it reduces the FVE into Sylvester form of algebraic equations which significantly simplify the problem. Error as well as convergence analysis of the proposed scheme are shown. Numerical results are discussed taking different initial conditions and wave velocities involved in the problem. Numerical results obtained by using suggested numerical algorithm are compared with the existing analytical methods for the different cases of FVE. (C) 2017 Elsevier Ltd. All rights reserved.
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