A Class of Colloction Method for Solving Fredholm Integral Equations Based on Ramp Function

A class of interpolation operator is constructed based on the ramp function, and the collocation scheme for solving the second kind linear Fredholm integral equations are obtained by discretizing the original continuous system. By generalizing the comparison theorem for Volterra integral equations to the case of Fredholm integral equations, and combining the resolvent representation theorem, the global convergence of the numerical scheme is proved strictly. Finally, the effectiveness of the scheme is verified by comparing the numerical and the analytic solution of several typical numerical experiments.