The Numerical Methods Of Quantum Zakharov Equations

In this paper, we mainly discuss two numerical solutions of quantum Zakharovequations: energy-preserving difference scheme and Predictor-Corrector scheme. Forenergy-preserving difference scheme, we firstly construct the numerical scheme, andtheoretically prove that this scheme meets the conservation law. Based on this, weprove the stability and convergence of this scheme. Then we introduce the Predictor-Corrector scheme, and construct the Predictor-Corrector scheme for the energy-preserv-ing difference scheme above. Also we prove the conservation law of it. Finally, forthe above two schemes, we do the numerical experiments, and compare the numericalsolution and exact solutions results, which show that the two schemes can have highaccuracy, and be good.