Efficient energy preserving Galerkin–Legendre spectral methods for fractional nonlinear Schrödinger equation with wave operator

Abstract

In this paper, three energy preserving numerical methods are proposed, including the Crank–Nicolson Galerkin–Legendre spectral (CN–GLS) method, the SAV Galerkin–Legendre spectral (SAV–GLS) method, and the ESAV Galerkin–Legendre spectral (ESAV–GLS) method, for the space fractional nonlinear Schrödinger equation with wave operator. In theoretical analyses, we take the CN–GLS method as an example to analyze the boundness of numerical solution and the unconditional spectral–accuracy convergence in L2 and L∞ norms. The effective numerical implementations of the proposed spectral Galerkin methods are discussed in detail. Numerical comparisons are reported to illustrate that the theoretical results are reasonable and the proposed spectral Galerkin methods have high efficiency for energy preservation in long–time computations.