A Fast Method for the Solution of Fredholm Integral Equations

Methods described to date for the solution of linear Fredholmintegral equations have a computing time requirement of O(N³),where N is the number of expansion functions or discretizationpoints used. We describe here a Tchebychev expansion method,based on the FFT, which reduces this time to O(N² ln N), andreport some comparative timings obtained with it. We give alsoboth a priori and a posteriori error estimates which are cheapto compute, and which appear more reliable than those used previously.