Método conservativo de diferencias finitas de alto orden para una clase de sistemas de Schrödinger no lineales

A time method to approximate the solution of a class of nonlinear Schrödinger systems, which preserves the power of each component and the Hamiltonian of the system exactly, is presented. Spatial discretizations based on fourth- and sixth-order explicit and compact finite difference formulas are considered; however, higher order formulas could also be used. The time advancing technique is based on a modification of a conservative Crank-Nicolson scheme, which is applied sequentially to each of the components of the vector field. Conservation of discrete invariants and order of convergence of the method are validated by means of a series of numerical experiments using different nonlinear potentials.