A general conservative eighth-order compact finite difference scheme for the coupled Schrödinger-KdV equations

In this paper, we present a general conservative eighth-order compact finite difference scheme for solving the coupled Schrödinger-KdV equations numerically. The proposed scheme is decoupled and preserves several physical invariants in discrete sense. The matrices obtained in the eighth-order compact scheme are all circulant symmetric positive definite so that it can be used to solve other similar equations. Numerical experiments on model problems show the better performance of the scheme compared with other numerical schemes.