High-order finite difference schemes for differential equations containing higher derivatives

In this paper, we evaluate the high-order finite difference schemes (both explicit and compact tridiagonal types) in conjunction with high-order low-pass filter for problems involving the fourth and fifth derivatives. Unconditional stability is proved. Extensive numerical experiments are carried out for two examples solved previously by local discontinuous Galerkin methods. The filtering is found necessary for achieving high accuracy over long time simulation when solving the fifth-order problem on finer meshes. Our numerical results show that very high accuracy can be obtained very efficiently by the high-order difference schemes coupling with the low-pass filter.