On the approximate solution of some Fredholm integral equations by Newton's method.
On the approximate solution of the multi-group time-dependent transport equation by -method
This paper concerns -velocity model of the general linear time-dependent transport equation. The assumed probability of the collision (scattering, fission) depends only on the angle of the directions of the moving neutron before and after the collision. The weak formulation of the problem is given and a priori estimates are obtained. The construction of an approximate problem by -method is given. In the symmetric hyperbolic system obtained by -method dissipativity and -orthogonality of the relevant...
On the approximative solution of integral equations
On the Aronszajn property for integral equations in Banach space
For the integral equation (1) below we prove the existence on an interval of a solution with values in a Banach space , belonging to the class , . Further, the set of solutions is shown to be a compact one in the sense of Aronszajn.
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 Boundedness and the Asymptotic Behaviour of the Non-Negative Solutions of Volterra-Hammerstein Integral Equations.
On the boundedness of Cauchy singular operator from the space to .
On the boundness of the Stokes semigroup in two-dimensional exterior domains.
On the buckling of a viscoelastic rod
On the Convergence of a Quadrature Rule for Evaluating Certain Cauchy Principal Value Integrals: An Addendum.
On the Convergence of Multi-Grid Methods for a Hypersingular Integral Equation of the First Kind.
On the convergence of Neumann series for noncompact operators
On the Convergence of the Galerkin Method for Nonsmooth Solutions of Integral Equations.
On the convolution equations over the quarter-plane.
On the Dirichlet and Neumann problems in multi-dimensional cone
We consider an elliptic pseudodifferential equation in a multi-dimensional cone, and using the wave factorization concept for an elliptic symbol we describe a general solution of such equation in Sobolev-Slobodetskii spaces. This general solution depends on some arbitrary functions, their quantity being determined by an index of the wave factorization. For identifying these arbitrary functions one needs some additional conditions, for example, boundary conditions. Simple boundary value problems,...
On the dynamics of a nonlinear multidimensional oscillator with memory.
On the dynamics of Bose-Einstein condensation
On the efficient use of the Galerkin-method to solve Fredholm integral equations
In the present paper we describe, how to use the Galerkin-method efficiently in solving boundary integral equations. In the first part we show how the elements of the system matrix can be computed in a reasonable time by using suitable coordinate transformations. These techniques can be applied to a wide class of integral equations (including hypersingular kernels) on piecewise smooth surfaces in 3-D, approximated by spline functions of arbitrary degree. In the second part we show, how to use the...
On the Eigenproblem for Convolution Integral Equations.