The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numericalmethod and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventionalmulti-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.
In this paper,a new symmetric energy-conserved splitting FDTD scheme(symmetric EC-S-FDTD)for Maxwell’s equations is proposed.The new algorithm inherits the same properties of our previous EC-S-FDTDI and EC-S-FDTDII algorithms:energy-conservation,unconditional stability and computational efficiency.It keeps the same computational complexity as the EC-S-FDTDI scheme and is of second-order accuracy in both time and space as the EC-S-FDTDII scheme.The convergence and error estimate of the symmetric EC-S-FDTD scheme are proved rigorously by the energy method and are confirmed by numerical experiments.
