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- W2277161103 abstract "Abstract In this paper we consider the one-dimensional nonlinear Schrödinger equation. The equation includes an absorption term, and the solution is periodically amplified in order to compensate the lose of the energy. The problem describes propa- gation of a signal in optical fibers. In our previous work we proved that the well-known Crank—Nicolson scheme is unconditionally unstable for this problem. We present in this paper two finite difference approximations. The first one is given by a modified Crank—Nicolson scheme and the second one is obtained by a splitting scheme. The stability and convergence of these schemes are proved. The results of numerical exper- iments are presented and discussed." @default.
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- W2277161103 date "2001-01-01" @default.
- W2277161103 modified "2023-09-27" @default.
- W2277161103 title "Numerical Approximation of The Weakly Damped Nonlinear Schrödinger Equation" @default.
- W2277161103 doi "https://doi.org/10.2478/cmam-2001-0021" @default.
- W2277161103 hasPublicationYear "2001" @default.
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