Compact Local Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation with Wave Operator - Huang, Langyang; Cai, Yaoxiong; Tian, Zhaowei (Mathematical problems in engineering, 2020)
Combining the compact method with the structure-preserving algorithm, we propose a compact local energy-preserving scheme and a compact local momentum-preserving scheme for the nonlinear Schrödinger equation with wave operator (NSEW). The convergence rates of both schemes are Oh4+τ2. The discrete local conservative properties of the presented schemes are derived theoretically. Numerical experiments are carried out to demonstrate the convergence order and local conservation laws of the developed algorithms.