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Numerical treatment of a well-posed Chebyshev Tau method for Bagley-Torvik equation with high-order of accuracy

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Abstract

The main purpose of this study is to develop and analyze a new high-order operational Tau method based on the Chebyshev polynomials as basis functions for obtaining the numerical solution of Bagley-Torvik equation which has a important role in the fractional calculus. It is shown that some derivatives of the solutions of these equations have a singularity at origin. To overcome this drawback we first change the original equation into a new equation with a better regularity properties by applying a regularization process and thereby the operational Chebyshev Tau method can be applied conveniently. Our proposed method has two main advantages. First, the algebraic form of the Tau discretization of the problem has an upper triangular structure which can be solved by forward substitution method. Second, Tau approximation of the problem converges to the exact ones with a highly rate of convergence under a more general regularity assumptions on the input data in spite of the singularity behavior of the exact solution. Numerical results are presented which confirm the theoretical results obtained and efficiency of the proposed method.

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  1. Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran

    P. Mokhtary

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  1. P. Mokhtary
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Mokhtary, P. Numerical treatment of a well-posed Chebyshev Tau method for Bagley-Torvik equation with high-order of accuracy. Numer Algor 72, 875–891 (2016). https://doi.org/10.1007/s11075-015-0072-9

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  • DOI: https://doi.org/10.1007/s11075-015-0072-9

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