Search

Your search keyword '"Abdelhakem, M."' showing total 14 results
Start Over Author "Abdelhakem, M." Search Limiters Peer Reviewed
14 results on '"Abdelhakem, M."'

3. Spectral Monic Chebyshev Approximation for Higher Order Differential Equations

Author

Abdelhakem, M., Ahmed, Aya, and El-kady, M.

Subjects
Mathematics - Numerical Analysis
Abstract

This paper is focused on performing a new method for solving linear and nonlinear higher-order boundary value problems (HBVPs). This direct numerical method based on spectral method. The trial function of this method is the Monic Chebyshev polynomials (MCPs). This method was relying on derivative of MCPs which explicit in the series expansion. The advantage of this method is solved HBVPs without transforming it to a system of lower-order ordinary differential equations (ODEs). This method supported by examples of HBVPs in wide application. The mentioned examples showed that the proposed method is efficient and accurate.

Published
2021
Full Text
View/download PDF

4. Shifted Monic Ultraspherical Approximation for solving some of Fractional Orders Differential Equations

Author

Abdelhakem, M., R., Doha M., Saadallah, A. F., and El-Kady, M.

Subjects
Mathematics - Numerical Analysis
Abstract

The purpose of this paper is to show and explain a new formula that indicates with finality the derivatives of Shifted Monic Ultraspherical polynomials (SMUPs) of any degree and for any fractional-order using the shifted Monic Ultraspherical polynomials themselves. We also create a direct method solution for the linear or nonlinear multi-order fractional differential equations (FDEs) with constant coefficients involving a spectral Galerkin method. The spatial approximation with its fractional order derivatives (described in the Caputo sense) are built using shifted Monic Ultraspherical polynomials.

Published
2021

8. Solving real-life BVPs via the second derivative Chebyshev pseudo-Galerkin method.

Author

Gamal, Marwa, El-Kady, M., and Abdelhakem, M.

Subjects
NONLINEAR boundary value problems, CHEBYSHEV polynomials, COLLOCATION methods
Abstract

The aim of this paper is to use the second derivative of Chebyshev polynomials (SDCHPs) as basis functions for solving linear and nonlinear boundary value problems (BVPs). Then, the operational matrix for the derivative was established by using SDCHPs. The established matrix via mixing between two spectral methods, collocation and Galerkin, has been applied to solve BVPs. Consequently, an error analysis is investigated to ensure the convergence of the technique used. Finally, we solved some problems involving real-life applications and compared their solutions with exact and other solutions from different methods to verify the accuracy and efficiency of this method. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

10. Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems.

Author

Abdelhamid, Dina, Albalawi, Wedad, Nisar, Kottakkaran Sooppy, Abdel-Aty, A., Alsaeed, Suliman, and Abdelhakem, M.

Subjects
CHEBYSHEV polynomials, BOUNDARY value problems, INITIAL value problems, ORDINARY differential equations
Abstract

A new form of basis functions structures has been constructed. These basis functions constitute a mix of Chebyshev polynomials and Legendre polynomials. The main purpose of these structures is to present several forms of differentiation matrices. These matrices were built from the perspective of pseudospectral approximation. Also, an investigation of the error analysis for the proposed expansion has been done. Then, we showed the presented matrices' efficiency and accuracy with several test functions. Consequently, the correctness of our matrices is demonstrated by solving ordinary differential equations and some initial boundary value problems. Finally, some comparisons between the presented approximations, exact solutions, and other methods ensured the efficiency and accuracy of the proposed matrices. [ABSTRACT FROM AUTHOR]

Published
2023
Full Text
View/download PDF

12. Approximating system of ordinary differential-algebraic equations via derivative of Legendre polynomials operational matrices.

Author

Abdelhakem, M., Baleanu, D., Agarwal, P., and Moussa, Hanaa

Subjects
*DIFFERENTIAL-algebraic equations, *MATRICES (Mathematics), *LEGENDRE'S polynomials, *POLYNOMIALS
Abstract

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. [ABSTRACT FROM AUTHOR]

Published
2023
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results