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Your search keyword '"El-Hawary, H. M."' showing total 26 results
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26 results on '"El-Hawary, H. M."'

3. Spectral Theory and Numerical Approximation for Singular Fractional Sturm-Liouville eigen-Problems on Unbounded Domain

Author

Aboelenen, T. and El-Hawary, H. M.

Subjects
Mathematics - Numerical Analysis
Abstract

In this article, we first introduce a singular fractional Sturm-Liouville eigen-problems (SFSLP) on unbounded domain. The associated fractional differential operators in these problems are both Weyl and Caputo type . The properties of spectral data for fractional operators on unbounded domain has been investigated. Moreover, it has been shown that the eigenvalues of the singular problems are real-valued and the corresponding eigenfunctions are orthogonal. The analytical eigensolutions to SFSLP is obtained and defined as generalized Laguerre fractional-polynomials. The optimal approximation of such generalized Laguerre fractional-polynomials in suitably weighted Sobolev spaces involving fractional derivatives has been derived, which is also available for approximated fractional-polynomials growing fast at infinity. The obtained results demonstrate that the error analysis beneficial of fractional spectral methods for fractional differential equations on unbounded domains. As a numerical example, we employ the new fractional-polynomials bases to demonstrate the exponential convergence of the approximation in agreement with the theoretical results., Comment: This paper has been withdrawn by the author due to a crucial sign error in equation 1

Published
2014

4. High-Order Chebyshev Pseudospectral Tempered Fractional Operational Matrices and Tempered Fractional Differential Problems.

Author

El-Abed, Amel, Dahy, Sayed A., El-Hawary, H. M., Aboelenen, Tarek, and Fahim, Alaa

Subjects
MATRICES (Mathematics), FRACTIONAL differential equations, DIFFERENTIAL operators, INTEGRAL operators, BURGERS' equation
Abstract

This paper focuses on presenting an accurate, stable, efficient, and fast pseudospectral method to solve tempered fractional differential equations (TFDEs) in both spatial and temporal dimensions. We employ the Chebyshev interpolating polynomial for g at Gauss–Lobatto (GL) points in the range [ − 1 , 1 ] and any identically shifted range. The proposed method carries with it a recast of the TFDE into integration formulas to take advantage of the adaptation of the integral operators, hence avoiding the ill-conditioning and reduction in the convergence rate of integer differential operators. Via various tempered fractional differential applications, the present technique shows many advantages; for instance, spectral accuracy, a much higher rate of running, fewer computational hurdles and programming, calculating the tempered-derivative/integral of fractional order, and its spectral accuracy in comparison with other competitive numerical schemes. The study includes stability and convergence analyses and the elapsed times taken to construct the collocation matrices and obtain the numerical solutions, as well as a numerical examination of the produced condition number κ (A) of the resulting linear systems. The accuracy and efficiency of the proposed method are studied from the standpoint of the L 2 and L ∞ -norms error and the fast rate of spectral convergence. [ABSTRACT FROM AUTHOR]

Published
2023
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23. An optimal ultraspherical approximation of integrals

Author

El-Hawary, H. M., Salim, M. S., and Hussien, H. S.

Abstract

In this paper some useful properties of the ultraspherical polynomials are derived. An ultraspherical approximation of any continuous function is presented. An ultraspherical approximation of finite integrals is introduced. The error estimation for the ultraspherical approximation is derived. An algorithm that gives an optimal approximation of the integrals is introduced. Numerical results are included to confirm the efficiency and accuracy of the method.

Published
2000
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24. Legendre spectral method for solving integral and integro-differential equations

Author

El-Hawary, H. M., Salim, M. S., and Hussein, H. S.

Abstract

A new spectral approximation of an integral based on Legendre approximation at the zeros of the first term of the residual is presented. The method is used to solve integral and integro-differential equations. The method generates approximations to the lower order derivatives of the function through successive integrations of the Legendre polynomial approximation to the highest order derivative. Numerical results are included to confirm the efficiency and accuracy of the method.

Published
2000
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25. A chebyshev method for the solution of boundary value problems

Author

Nasr, H. and El-Hawary, H. M.

Abstract

An expansion procedure using the Chebyshev polynomials is proposed by using El-Gendi method [1], which yields more accurate results than those computed by D. Hatziavrmidis [2] as indicated from solving the Orr-Sommerfeld equation for both the plane poiseuille flow and the Blasius velocity profile. This method is accomplished by starting with Chebyshev approximation for the highest-order derivative and generating approximations to the lower-order derivatives through integration of the highest-order derivative.

Published
1991
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