Spline function approximations to the solution of singular Volterra integral equations of the second kind

An arbitrarily high-order method for the approximate solution of singular Volterra integral equations of the second kind is presented. The approximate solution is a spline function of degree m, deficiency (m-1), i.e. in the continuity class C, and the method is of order m+1. For m=2 and 3 the method is modified so that the approximate solution is in C/sup 1/. Moreover, an investigation of numerical stability is given and it is shown that, while the above cited methods are numerically stable, methods using spline functions with full continuity are divergent for all m>or=3. (9 refs).