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Semidiscretization in time for nonlinear Schrödinger-wave equations. (English) Zbl 0976.76054
Summary: We are concerned with Crank-Nicolson like schemes for the equation \({1\over \omega^2} \partial^2_t E_\omega-i \partial_tE_\omega-\Delta E_\omega= \lambda|E_\omega |^{2\sigma} E_\omega\). We present two schemes for which we give convergence results. One of the scheme is dissipative, and we descrie precisely the dissipation. We prove that the solution by the second scheme fits with the exact solution, while the first one computes an average value of the solutions.

76M20 Finite difference methods applied to problems in fluid mechanics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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