Collocation methods for nonlinear Volterra integral equations with oscillatory kernel

In this paper, we consider the second kind of Nonlinear Volterra integral equation with a highly oscillatory kernel. An exact Collocation method is constructed and then the oscillatory integrals in the exact collocation are discretized by a Filon type method. We analyze the convergence of the method based on some lemmas and theorems. In the last, the efficiency of the proposed methods is numerically and analytically analyzed