QUADRATURE FORMULAE FOR THE CALCULATION OF INTEGRALS WITH WEAKLY SINGULAR KERNELS: APPLICATIONS IN THE SOLUTION OF CAUCHY INTEGRAL EQUATIONS

Maurílio BOAVENTURA[1]

José Alberto CUMINATO[2]

§    ABSTRACT: This paper is concerned with the study of a quadrature formulae to approximate integrals of the form : log½ x –t½ g(t) dt, where g is a continuous function. This quadrature formulae is then used in the solution of the singular integral equation: k(x, t) f (t)dt = f(x), k(x, t) k1(x, t) + k2(x, t) log½ x –t½ .

§    KEYWORDS: Quadrature formulae; singular integral equation; Cauchy equation

 

 



[1] Departamento de Ciências da Computação e Estatística - Instituto de Biociências, Letras e Ciências Exatas - UNESP - 15054-000 São José do Rio Preto - SP - Brasil.

[2] Departamento de Ciências da Computação e Estatística - Instituto de Ciências Matemáticas de São Carlos - USP – 13560-970 - São Carlos - SP - Brasil.