The author develops four types of quadrature formulae for the numerical solution of Fredholm integral equations of the form \(\omega f(t)+\int K(t,x)f(x)dx=g(t)\) (a\(\leq t\leq b)\), where K, g and (hence) f have period b-a and \(\omega\) is either 0 or 1. The kernel K is assumed to be weakly singular, with particular attention being given to kernels which can be written in the form \(H_ 1(t,x)\ln | t-x| +H_ 2(t,x).\) All the formulae are based on the trapezoidal rule with equidistant abscissae, and asymptotic expansions are derived for their respective errors.
Comparison is made of their implementations in respect of their computational cost, accuracy, and efficiency when used in conjunction with the Richardson extrapolation. It is concluded that the formula which was developed by the author and M. Israeli in a previous paper [J. Sci. Comput. 3, No.2, 201-231 (1988; Zbl 0662.65122)] is the most advantageous. A description of the numerical solution of a particular inhomogeneous equation of the second kind concludes the paper.