Browsing by Author "Alzahrani, A. A."

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Citation Count: Bhrawy, A.H...et al. (2016). A chebyshev-laguerre-gauss-radau collocation scheme for solving a time fractional sub-diffusion equation on a semi-infinite domain. Proceedings Of The Romanian Academy Series A-Mathematics Physics Technical Science Information Science, 16(4), 490-498.
A chebyshev-laguerre-gauss-radau collocation scheme for solving a time fractional sub-diffusion equation on a semi-infinite domain
(The Publishing House of the Romanian Academy, 2015) Bhrawy, A. H.; Abdelkawy, M. A.; Alzahrani, A. A.; Baleanu, Dumitru; Alzahrani, Ebraheem
We propose a new efficient spectral collocation method for solving a time fractional sub-diffusion equation on a semi-infinite domain. The shifted Chebyshev-Gauss-Radau interpolation method is adapted for time discretization along with the Laguerre-Gauss-Radau collocation scheme that is used for space discretization on a semi-infinite domain. The main advantage of the proposed approach is that a spectral method is implemented for both time and space discretizations, which allows us to present a new efficient algorithm for solving time fractional sub-diffusion equations
Citation Count: Bhrawy, A.H...et al. (2015). Generalized Laguerre-Gauss-Radau scheme for first order hyperbolic equations on semi-infinite domains. Romanian Journal of Physics, 60(7-8), 918-934.
Generalized Laguerre-Gauss-Radau scheme for first order hyperbolic equations on semi-infinite domains
(Editura Academiei Romane, 2015) Bhrawy, A. H.; Hafez, R. M.; Alzahrani, Ebraheem; Baleanu, Dumitru; Alzahrani, A. A.
In this article, we develop a numerical approximation for first-order hyperbolic equations on semi-infinite domains by using a spectral collocation scheme. First, we propose the generalized Laguerre-Gauss-Radau collocation scheme for both spatial and temporal discretizations. This in turn reduces the problem to the obtaining of a system of algebraic equations. Second, we use a Newton iteration technique to solve it. Finally, the obtained results are compared with the exact solutions, highlighting the performance of the proposed numerical method.