Solution of Fredholm Equations with Symmetric Difference Kernels

A simple numerical procedure is outlined for the solution ofFredholm equations with symmetric difference kernels. By retainingthe properties of symmetry and convolution in the approximatingdiscrete system we obtain a set of equations identical in formto the normal equations arising in the prediction of stationarytime series. A standard recursive method allows us to work withlarge systems of equations, the resulting fineness of the meshpermitting accurate solutions. An alternative method of solvingthe same normal equations is based on the Wiener-Hopf procedureand may be more efficient than the recursive method for verylarge systems.