Fast numerical solution of fredholm integral equations with stationary kernels

A fast recursive matrix method for the numerical solution of Fredholm integral equations with stationary kernels is derived. IfN denotes the number of nodal points, the complexity of the algorithm isO(N ²), which should be compared toO(N ³) for conventional algorithms for solving such problems. The method is related to fast algorithms for inverting Toeplitz matrices.Applications to equations of the first and second kind as well as miscellaneous problems are discussed and illustrated with numerical examples. These show that the theoretical improvement in efficiency is indeed obtained, and that no problems with numerical stability or accuracy are encountered.