A Central Part Interpolation Scheme for Log-Singular Integral Equations

Abstract

A fully 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 “central part” interpolation by polynomials on the uniform grid.

Keywords:

• weakly singular integral equations
• logarithmic diagonal singularity
• collocation method
• product integration
• central part interpolation

AMS Subject Classification:

• 65R20
• 65D05
• 65D07
• 65D30