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.
On the Convergence of the Nyström Method for the Integral Equation Eigenvalue Problem.
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.
On the Fast Matrix Multiplication in the Boundary Element Method by Panel Clustering.
On the integration schemes of retrieving impulse response functions from transfer functions.
On the Inversion of the Attenuated Radon Transform.
On the Numerical Resolution of the Generalized Airfoil Equation with Possio Kernel.
On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation.
On the numerical solution of an Abel integral equation
On the numerical solution of the generalized Abel integral equation
On the numerical solution of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity.
On the order of pointwise convergence of some boundary element methods. Part I. Operators of negative and zero order
On the quadrature error in operational quadrature methods for convolutions.
On the question of enclosing solutions of linear functional-differential systems.
On the Regularization of Projection Methods for Solving Ill-Posed Problems.