Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 867-874
For the class of multidimensional Fredholm integral equations with free terms and kernels periodic and harmonic in each variable, we determine the exact order of the minimum radius of information in the logarithmic scale.
Ukr. Mat. Zh. - 1997. - 49, № 9. - pp. 1157–1161
We propose a direct method for the approximate solution of integral equations that arise in the course of approximate solution of a periodic boundary-value problem for linear differential equations by the method of boundary conditions. We show that the proposed direct method is optimal in order.
On the optimal rate of convergence of the projection-iterative method and some generalizations of it on a class of equations with smoothing operators
Ukr. Mat. Zh. - 1996. - 48, № 11. - pp. 1448-1456
For some classes of operator equations of the second kind with smoothing operators, we find the exact order of the optimal rate of convergence of generalized projection-iterative methods.
On the complexity of boundary integral equations with analytic coefficients with logarithmic singularities
Ukr. Mat. Zh. - 1996. - 48, № 10. - pp. 1299-1310
We find the exact order of the ε-complexity of weakly singular integral equations with periodic and analytic coefficients of logarithmic singularities. This class of equations includes boundary equations for outer boundary-value problems for the two-dimensional Helmholtz equation.
Optimal methods for specifying information in the solution of integral equations with analytic kernels
Ukr. Mat. Zh. - 1996. - 48, № 5. - pp. 656-664
We determine the exact order of the minimum radius of information in the logarithmic scale for Fredholm integral equations of the second kind with periodic analytic kernels and free terms. We show that the information complexity of the solution of Fredholm equations with analytic kernels is greater in order than the complexity of the approximation of analytic functions. This distinguishes the analytic case from the case of finite smoothness.