On the implementation of discontinuous Galerkin methods for Volterra integral equations with highly oscillatory Bessel kernels

摘要

In this paper, we consider implementation of discontinuous Galerkin methods for (weakly singular) Volterra integral equations of first and second kinds with highly oscillatory Bessel kernels, which cost the same operations independent of large values of frequencies. Preliminary numerical results show that the proposed method is efficient for verifying accuracy of approximate solutions.