A high-accuracy conservative numerical scheme for the generalized nonlinear Schrödinger equation with wave operator

Abstract

In this article, we establish a novel high-order energy-preserving numerical approximation scheme to study the initial and periodic boundary problem of the generalized nonlinear Schrödinger equation with wave operator, which is proposed by the finite difference method. The scheme is of fourth-order accuracy in space and second-order one in time. The conservation property of energy as well as a priori estimate are described. The convergence of the proposed scheme is discussed in detail by using the energy method. Some comparisons have been made between the proposed method and the others. Numerical examples are presented to illustrate the validity and accuracy of the method.

Keywords

• the nonlinear schrödinger equation with wave operator
• high-accuracy scheme
• conservative property
• error estimate
• convergence