Numerical method for a Schrödinger problem with amplification process - Čiegis, Raimondas; Kairytė, Genė; Pakalnytė, Violeta (Lietuvos matematikos rinkinys, 1999)
In this paper we consider one Schrödinger problem which describes a signal propagation in optical fibers. The stability of symmetrical finite difference scheme is investigated in the L2 norm. It is proved that the scheme becomes unstable if the signal is periodically amplified along the fiber. A modification of the symmetrical scheme and one splitting scheme are proposed to solve the given problem.