Browsing by Author "Abdelhakem, M."

Now showing 1 - 4 of 4

Citation - WoS: 19
Citation - Scopus: 22
Approximating System of Ordinary Differential-Algebraic Equations Via Derivative of Legendre Polynomials Operational Matrices
(World Scientific Publ Co Pte Ltd, 2023) Abdelhakem, M.; Baleanu, D.; Agarwal, P.; Moussa, Hanaa
Legendre polynomials' first derivatives have been used as the basis function via the pseudo-Galerkin spectral method. Operational matrices for derivatives have been used and extended to deal with the system of ordinary differential-algebraic equations. An algorithm via those matrices has been designed. The accuracy and efficiency of the proposed algorithm had been shown by two techniques, theoretically, via the boundedness of the approximated expansion and numerically through numerical examples.
Citation - WoS: 28
Citation - Scopus: 30
Monic Chebyshev Pseudospectral Differentiation Matrices for Higher-Order Ivps and Bvps: Applications To Certain Types of Real-Life Problems
(Springer Heidelberg, 2022) Abdelhakem, M.; Ahmed, A.; Baleanu, D.; El-kady, M.
We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in differentiation matrices (D-matrices). Those matrices have been used to approximate the solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be used in this work. The first technique is a direct approximation of the H-ODE. While the second technique depends on transforming the H-ODE into a system of lower order ODEs. We discuss the error analysis of these D-matrices in-depth. Also, the approximation and truncation error convergence have been presented to improve the error analysis. Some numerical test functions and examples are illustrated to show the constructed D-matrices' efficiency and accuracy.
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.