2019
Том 71
№ 6

All Issues

Rizk M. M.

Articles: 3
Article (English)

Dzyadyk's Technique for Ordinary Differential Equations Using Hermitian Interpolating Polynomials

Rizk M. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 4. - pp. 501-512

For the case of Hermitian interpolation, we consider the approximation-iterative method introduced by Dzyadyk. We construct a practical algorithm.

Article (English)

Expansions for the Fundamental Hermite Interpolation Polynomials in Terms of Chebyshev Polynomials

Rizk M. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 1. - pp. 135-143

We obtain explicit expansions of the fundamental Hermite interpolation polynomials in terms of Chebyshev polynomials in the case where the nodes considered are either zeros of the (n + 1)th-degree Chebyshev polynomial or extremum points of the nth-degree Chebyshev polynomial.

Article (English)

On the approximate solution of nonlinear Volterra-Fredholm integral equations on a complex domain by Dzyadyk’s method

Rizk M. M., Zaher S. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 11. - pp. 1519–1528

In 1980–1984, V. K. Dzyadyk suggested and modified an iterative approximation method (IA-method) for numerical solution of the Cauchy problem y′=f(x,y), y(x 0)=x0. Particular cases of nonlinear mixed Volterra-Fredholm integral equations of the second kind arise in the mathematical simulation of the space-time development of an epidemic. This paper is concerned with the approximate solution of integral equations of this type by the Dzyadyk method on complex domains. Finally, we test this method numerically by four different examples.