An Automatic Program for Linear Fredholm Integral Equations of the Second Kind

Two automatic programs for solving linear Fredholm integral equations of the second kind are described and illustrated.It is assumed that the kernel function and solution are smooth and that they are given analytically, not as discrete data.The numerical method is based on the Nystr6m method, with an lteratlve technique to solve the resulting linear systems.The main discussion centers on Simpson's method as the numerical integration rule.A powerful variant based on Gaussian quadrature m also discussed, and tests for ill-conditioned problems have been incorporated into the program.Modifiability of the Simpson program is also discussed. The Algorithm: Algorithm 503, An Automatic Program for Fredhohn Integral Equations of theSecond Kind.