A numerical method for a Volterra-type integral equation with logarithm kernel

We consider a class of integral equations of Volterra type with constant coefficients containing a logarithmic difference kernel. This class coincides for a=0 with the Symm's euqtion. We can transform the general integral equation into an equivalent singular equation of Cauchy type which allows us to give the explicit formula for the solution. The numerical method proposed in this paper consists in substituting this in the experrsion of the solution g. Then, with the aid of the inveriance properties of the orthogonal polynomials for the Cauchy integral equation, we obtain an approximate solution of the function g. We give weighted norm estimates for the error of this method. The paper concludes with some numerical examples.