A Class of Numerical Method for Solving Fredholm Integral Equations Based on Bernoulli Function

Based on the Bernoulli function and a non-uniform partition of the computational interval, an efficient algorithm for solving second-kind Fredholm integral equations is proposed. This method extends the classical Euler-Maclaurin summation formula and achieves a local convergence order of 2 under certain assumptions. Numerical experiments validate the theoretical convergence order of the constructed algorithm and demonstrate its high efficiency in solving singular integral equations.