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