关键词: Schrodinger方程, 变限积分法, 四阶Runge-Kutta法, 收敛性分析

Abstract: Firstly, the variable limit integral method and the fourth-order Runge-Kutta method were used to discretize the spatial and temporal variables of a nonlinear Schrodinger equation with a fifth order term, respectively, and a fully-discrete scheme for the initial boundary value problem was constructed. Secondly, we theoretically proved the boundedness, existence, uniqueness and the order of convergence of the numerical solution. Finally, the numerical simulations verified the validity of the theoretical analysis.

Key words: Schrodinger equation, variable integral method, fourth-order Runge-Kutta method, convergence analysis