ON FULLY DISCRETE COLLOCATION METHODS FOR SOLVING WEAKLY SINGULAR INTEGRAL EQUATIONS

Fully Discrete Collocation Method for Weakly Singular Integral Equations

Abstract. To find the approximate solutions of a weakly singular integral equation by the collocation method it is necessary to solve linear systems whose coefficients are expressed as integrals. These integrals cannot usually be computed exactly. We get the fully discrete collocation method when we approximate the integrals by quadrature formulas on nonuniform grid. In this paper an appropriat...

COLLOCATION METHOD FOR FREDHOLM-VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY KERNELS

In this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎Fredholm-Volterra integral equations (FVIEs) are smooth‎.

Discrete Collocation Method for Solving Fredholm Volterra Intergro-Differential Equations

A collocation method for solving integral equations

A collocation method is formulated and justified for numerical solution of the Fredholm second-kind integral equations. As an application the Lippmann-Schwinger equation is considered. The results obtained provide an error estimate and a justification of the limiting procedure used in the earlier papers by the author, dealing with many-body scattering problems in the case of small scatterers, a...

Direct methods for solving singular integral equations with complex conjugation

The computational schemes of collocation and mechanical quadrature methods for solving singular integral equations (S.I.E.) containing the complex conjugate unknown function are proposed in this paper. A theoretical foundation of these two methods is obtained in Hölder functions space Hβ (0 < β < 1) and in Lp, 1 < p < ∞ spaces. A rather common case of a nonstandard contour of integration is inv...