Product Quasi-Interpolation in Logarithmically Singular Integral Equations

Abstract

A discrete high order method is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have boundary and logarithmic diagonal singularities. The method is based on the improving the boundary behaviour of the kernel with the help of a change of variables, and on the product integration using quasi-interpolation by smooth splines of order m. Properties of different proposed calculation schemes are compared through numerical experiments using, in particular, variable precision interval arithmetics.

Keywords:

• weakly singular integral equations
• boundary singularities
• spline quasi-interpolation
• product integration
• Nyström-type methods

AMS Subject Classification:

• 65R20
• 65D07
• 65D30