Mass and energy conservative high-order diagonally implicit Runge–Kutta schemes for nonlinear Schrödinger equation

Abstract

We present and analyze a series of structure-preserving diagonally implicit Runge–Kutta schemes for the nonlinear Schrödinger equation. These schemes possess not only high accuracy, high order convergence (up to fifth order) and efficiency due to the diagonally implicity but also mass and energy conservative properties. Theoretical analysis and numerical experiments are conducted to verify the accuracy, invariant conservative properties and longtime simulation stability.