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- Eid H. Doha, Waleed M. Abd-Elhameed
- SIAM J. Scientific Computing
- 2002

- Eid H. Doha, Ali H. Bhrawy
- Numerical Algorithms
- 2006

It is well known that spectral methods (tau, Galerkin, collocation) have a condition number of $O(N^{4})$ ($N$ is the number of retained modes of polynomial approximations). This paper presents some… (More)

- Eid H. Doha, Ali H. Bhrawy
- Computers & Mathematics with Applications
- 2012

A new formula expressing explicitly the derivatives of Bernstein polynomials of any degree and for any order in terms of Bernstein polynomials themselves is proved, and a formula expressing the… (More)

- Eid H. Doha, Waleed M. Abd-Elhameed
- Mathematics and Computers in Simulation
- 2009

and Applied Analysis 3 Theorem 1. Thefirst derivative of second kind Chebyshev polynomials is given by

and Applied Analysis 3 respectively, of degree n. For our present purposes, it is more convenient to introduce the normalized orthogonal polynomials R α,β n x P α,β n x / P α,β n 1 . This means that… (More)

- Ali H. Bhrawy, Eid H. Doha, Dumitru Baleanu, Samer S. Ezz-Eldien
- J. Comput. Physics
- 2015

Article history: Received 11 January 2014 Received in revised form 7 March 2014 Accepted 23 March 2014 Available online xxxx

- Eid H. Doha, Ali H. Bhrawy, M. A. Saker
- Appl. Math. Lett.
- 2011

A new explicit formula for the integrals of Bernstein polynomials of any degree for any order in terms of Bernstein polynomials themselves is derived. A fast and accurate algorithm is developed for… (More)

- Eid H. Doha, Ali H. Bhrawy, Waleed M. Abd-Elhameed
- Numerical Algorithms
- 2008

This paper is concerned with fast spectral-Galerkin Jacobi algorithms for solving one- and two-dimensional elliptic equations with homogeneous and nonhomogeneous Neumann boundary conditions. The… (More)