We study a linear semidiscrete-in-time finite difference method for the system of nonlinear Schrödinger equations that is a model of the interaction of non-relativistic particles with different masses. The main aim is to show that the scheme is second-order convergent.
"A second-order time-discretization scheme for a system of nonlinear Schrödinger equations." Proc. Japan Acad. Ser. A Math. Sci. 90 (1) 15 - 20, January 2014. https://doi.org/10.3792/pjaa.90.15