On convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations.
On discrete approximations for a class of linear functional differential equations
On empirical stochastic regularization
On iterative solution of nonlinear functional equations in a metric space.
On Monotone Abel-Volterra Integral Equations on the Half Line.
On Multilevel Iterative Methods for Integral Equations of the Second Kind and Related Problems.
On numerical solution to the problem of reactor kinetics with delayed neutrons by Monte Carlo method
In this paper, the linear problem of reactor kinetics with delayed neutrons is studied whose formulation is based on the integral transport equation. Besides the proof of existence and uniqueness of the solution, a special random process and random variables for numerical elaboration of the problem by Monte Carlo method are presented. It is proved that these variables give an unbiased estimate of the solution and that their expectations and variances are finite.
On optimal regularization methods for fractional differentiation.
On projective methods of approximate solution of singular integral equations.
On quadrature methods for the double layer potential equation over the boundary of a polyhedron.
On rational classical orthogonal polynomials and their application for explicit computation of inverse Laplace transforms.
On Spline Galerkin Methods for Singular Integral Equations with Piecewise Continuous Coefficients.
On the approximate solution of nonlinear singular integral equations with positive index.
On the Approximate Solution of Operator Equations.
On the approximate solution of some Fredholm integral equations by Newton's method.
On the approximative solution of integral equations
On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations
We prove the convergence of polynomial collocation method for periodic singular integral, pseudodifferential and the systems of pseudodifferential equations in Sobolev spaces via the equivalence between the collocation and modified Galerkin methods. The boundness of the Lagrange interpolation operator in this spaces when allows to obtain the optimal error estimate for the approximate solution i.e. it has the same rate as the best approximation of the exact solution by the polynomials.
On the Boundary Element Method for Some Nonlinear Boundary Value Problems.
On the Convergence of Multi-Grid Methods for a Hypersingular Integral Equation of the First Kind.
On the Convergence of the Galerkin Method for Nonsmooth Solutions of Integral Equations.