Abstract
We propose explicit and conditionally stable combined numerical method based on using of both the conservative finite-difference scheme and non-conservative Rosenbrock method, for solving of 1D and 2D nonlinear Schrodinger equation. Each of these finite-difference schemes has own advantages and disadvantages. The conservative finite-difference scheme is implicit, conservative and possesses the property of asymptotic stability and the second order of approximation. The Rosenbrock method is conditionally conservative, explicit and possesses the same order of approximation in spatial coordinate only. Proposed finite-difference scheme is explicit and more effective for some cases.
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