High-order explicit conservative exponential integrator schemes for fractional Hamiltonian PDEs

Abstract

The paper aims to develop a class of high-order explicit exponential time differencing energy-preserving schemes for some conservative fractional PDEs based on the general Hamiltonian form of these equations. The equation is first reformulated into an equivalent system that possesses a new quadratic energy by introducing an auxiliary variable. Then, explicit schemes are derived via applying the exponential time differencing Runge-Kutta method approximations for time integration and Fourier pseudo-spectral discretization in space, which can maintain the accuracy and improve the stability to the system with stiffness. Subsequently, highly efficient energy-preserving schemes are given by combining the proposed explicit schemes and the projection technique. Finally, the advantages of the proposed schemes are illustrated by the numerical results of the fractional nonlinear Schrödinger equation.