Two-Dimensional Singular Fredholm Integral Equation with Applications in Contact Problems

Abstract

In this paper we discuss the solution of the Two-dimensional singular Fredholm integral equation (T-DFIE). The existence of a unique solution of the T-DFIE is discussed and proved using Banach Fixed point theorem. Then, using Toeplitz matrix method and Product Nystrom method, we obtain a linear algebraic system of equations (LAS). Some numerical cases, in contact problems when the kernel takes Cauchy kernel, logarithmic form and Carleman function, are solved.

Key words and phrases. two-dimensional singular Fredholm integral equation, Toeplitz matrix method, Product Nystrom method.

2000 Mathematics Subject Classification. Primary: 45B05 , Secondary: 45G10; 65R