Linearly implicit energy-preserving integrating factor methods and convergence analysis for the 2D nonlinear Schrödinger equation with wave operator

Abstract

Abstract In this paper, we develop a novel class of linearly implicit and energy-preserving integrating factor methods for the 2D nonlinear Schrödinger equation with wave operator (NLSW), combining the scalar auxiliary variable approach and the integrating factor methods. To begin, a second-order scheme is proposed, which is rigorously proved to be energy-preserving. By using the energy methods, we analyze its optimal convergence without any restrictions on the grid ratio, where a novel technique and an improved induction argument are proposed to circumvent the difficulty arising from the unavailability of a priori$L^{\infty }$ estimates of numerical solutions. Based on the integrating factor Runge–Kutta methods, we extend the proposed scheme to arbitrarily high order, which is also linearly implicit and conservative. Numerical experiments are presented to confirm the theoretical analysis and demonstrate the advantages of the proposed methods.