Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations

We propose a new procedure for designing finite-difference schemes that inherit energy conservation or dissipation property from complex-valued nonlinear partial differential equations (PDEs), such as the nonlinear Schrodinger equation, the Ginzburg-Landau equation, and the Newel I-Whitehead equation. The procedure is a complex version of the procedure that Furihata has recently presented for real-valued nonlinear PDEs. Furthermore, we show that the proposed procedure can be modified for designing "linearly implicit" finite-difference schemes that inherit energy conservation or dissipation property. (C) 2001 Academic Press.