Mass and energy conservative high order diagonally implicit Runge–Kutta schemes for nonlinear Schrödinger equation in one and two dimensions

10/30/2019

∙

by   Ziyuan Liu, et al.

∙

0

∙

share

We present and analyze a series of conservative diagonally implicit Runge–Kutta schemes for the nonlinear Schrödiner equation. With the application of the newly developed invariant energy quadratization approach, these schemes possess not only high accuracy , high order convergence (up to fifth order) and efficiency due to diagonally implicity but also mass and energy conservative properties. Both theoretical analysis and numerical experiments of one- and two-dimensional dynamics are carried out to verify the invariant conservative properties, convergence orders and longtime simulation stability.