Browsing by Author "Taha, T. M."

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Citation Count: Doha, E. H...et.al. (2017). "Composite Bernoulli-Laguerre collocation method for a class of hyperbolic telegraph-type equations", Romanian Reports In Physics, Vol.69, No.4.
Composite Bernoulli-Laguerre collocation method for a class of hyperbolic telegraph-type equations
(Editura Academiei Romane, 2017) Doha, E. H.; Hafez, R. M.; Abdelkawy, M. A.; Ezz-Eldien, S. S.; Taha, T. M.; Zaky, M. A.; Amin, A. Z. M.; El-Kalaawy, A. A.; Baleanu, Dumitru; 56389
In this work, we introduce an efficient Bernoulli-Laguerre collocation method for solving a class of hyperbolic telegraph-type equations in one dimension. Bernoulli and Laguerre polynomials and their properties are utilized to reduce the aforementioned problems to systems of algebraic equations. The proposed collocation method, both in spatial and temporal discretizations, is successfully developed to handle the two-dimensional case. In order to highlight the effectiveness of our approachs, several numerical examples are given. The approximation techniques and results developed in this paper are appropriate for many other problems on multiple-dimensional domains, which are not of standard types.
Citation Count: Baleanu, D.; Bhrawy, A. H.; Taha, T. M. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems", Abstract and Applied Analysis, (2013)
Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems
(Hindawi LTD, 2013) Baleanu, Dumitru; Bhrawy, A. H.; Taha, T. M.; 56389
We present a direct solution technique for approximating linear multiterm fractional differential equations (FDEs) on semi-infinite interval, using generalized Laguerre polynomials. We derive the operational matrix of Caputo fractional derivative of the generalized Laguerre polynomials which is applied together with generalized Laguerre tau approximation for implementing a spectral solution of linear multitermFDEs on semi-infinite interval subject to initial conditions. The generalized Laguerre pseudo-spectral approximation based on the generalized Laguerre operational matrix is investigated to reduce the nonlinear multiterm FDEs and its initial conditions to nonlinear algebraic system, thus greatly simplifying the problem. Through several numerical examples, we confirm the accuracy and performance of the proposed spectral algorithms. Indeed, the methods yield accurate results, and the exact solutions are achieved for some tested problems.