Solution of Non-Linear Fredholm Integral Equations by a Variational Approach

摘要

A method for the numerical solution of nonlinear Fredholm integral equations, based on a suitable variational principle, is considered. The relation between the suggested method and existing methods is investigated in terms of the variational principle, and a measure of the convergence rate is obtained. All inner products were computed by Clenshaw Curtis quadrature except in the case of singular integrals where the transformation methods of Evans, Forbes, and Hyslop are used. The method was tested on a number of examples including a particularly difficult one due to Cohen. The method demonstrates robustness without loss of speed compared with previous techniques.