The Nyström Method and Convergence Analysis for System of Fredholm Integral Equations

In this paper, the efficient numerical solutions of a class of system of Fredholm integral equations are solved by the Nystrom method, which discretizes the system of integral equations into solving a linear system. The existence and uniqueness of the exact solutions are proved by the Banach fixed point theorem. The format of the Nystrom solutions is given, especially with the composite Trapezoidal and Simpson rules. The results of error estimation and convergence analysis are obtained in the infinite norm sense. The validity and reliability of the theoretical analysis are verified by numerical experiments.