Abstract
In this paper, we have presented an accurate and impressive spectral algorithm for solving fractional telegraph equation with Riesz-space derivative and Dirichlet boundary conditions. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrices of Riemann–Liouville fractional integral and left- and right-sided Caputo fractional derivatives. Primarily, we implement the proposed algorithm in both temporal and spatial discretizations. This algorithm reduces the problem to a system of algebraic equations which considerably simplifies the problem. In addition, an error bound is established in the \(L^{\infty }\)-norm for the suggested spectral Jacobi tau method. Illustrative examples are included to demonstrate the validity and accuracy of the presented technique.
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Communicated by José Tenreiro Machado.
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Bonyadi, S., Mahmoudi, Y., Lakestani, M. et al. A tau method based on Jacobi operational matrix for solving fractional telegraph equation with Riesz-space derivative. Comp. Appl. Math. 39, 309 (2020). https://doi.org/10.1007/s40314-020-01363-9
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DOI: https://doi.org/10.1007/s40314-020-01363-9