NUMERICAL TREATMENT OF FREDHOLM INTEGRAL EQUATIONS OVER $(0, infty$ USING HILBERT TRANSFORM

Abstract

In this paper, we present two types of integral equations of the second kind over semiaxis. Then we introduce a new numerical method by using the product rule, Nyström method and Hilbert Transform and prove that the proposed procedures are stable and convergent. The method reduces the integral equation to a system of linear algebraic equations. Some numerical examples are presented to show the efficiency and accuracy of the method.