Browsing by Author "El-Kady, M."

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Citation - Scopus: 27
A Numerical Method Based on Legendre Differentiation Matrices for Higher Order Odes
(Natural Sciences Publishing, 2020) Biomy, M.; Kandil, S.A.; Baleanu, D.; El-Kady, M.; Abdelhakem, M.
This paper introduces a new method to obtain the spectral accuracy solutions to higher order differential equations and singularly perturbed boundary value problems (BVPs). Legendre polynomials (LPs) Pn (x) have been used and involved in straightforward implementation method. Asymptotic upper bound on the Legendre coefficients for the kt h derivatives are presented. Also, We detect the roundoff error effect in the Legendre matrices. The superiority of the suggested method became evident through some examples and applications. © 2020 NSP Natural Sciences Publishing Cor.
Citation - WoS: 34
Citation - Scopus: 39
Shifted Chebyshev Schemes for Solving Fractional Optimal Control Problems
(Sage Publications Ltd, 2019) Moussa, H.; Baleanu, D.; El-Kady, M.; Abdelhakem, M.
Two schemes to find approximated solutions of optimal control problems of fractional order (FOCPs) are investigated. Integration and differentiation matrices were used in these schemes. These schemes used Chebyshev polynomials in the shifted case as a functional approximation. The target of the presented schemes is to convert such problems to optimization problems (OPs). Numerical examples are included, showing the strength of the schemes.