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Arbitrarily high order uniformly accurate algorithms for the Zakharov system in the subsonic limit regime

组织者

李震 , 梁鑫 , 马志婷 , 哈米德·莫菲迪 , 王丽 , 熊繁升 , 杨朔 , 杨武岳

演讲者

周旋旋

时间

2025年05月15日 15:00 至 16:00

地点

Online

线上

Zoom 787 662 9899 (BIMSA)

摘要

In this talk, We develop fully discrete uniformly numerical methods of arbitrarily high order for the nonlinear Zakharov system (ZS) in the subsonic limit regime with a dimensionless parameter 0 < γ ≤ 1, which are inversely proportional to the acoustic speed. In the subsonic limit regime, i.e., 0 < γ ≪ 1, the solutions have highly oscillatory waves and outgoing initial layers due to the perturbation from wave operator in ZS and the incompatibility of the initial data. The high oscillation brings noticeable difficulties in constructing accurate and efficient method and analyzing the error bounds of numerical methods to the ZS. In this work, by using the Duhamel’s principle and integration by parts in time, we reformulate the differential equations (1.1) into integral form. For the reformulated model, we apply nested Picard iterative integrator in time to arrive at a semi-discrete system, then we use Fourier pseudospectral method and phase-space analysis method to propose fully discrete uniformly convergence schemes which is explicit, high-order and easily expanded. Detailed constructions of the NPI methods up to the second order in time are presented for ZS, where the corresponding error estimates are rigorously analyzed. In addition, the practical implementation of the second-order NPI method via Fourier pseudospectral discretization is clearly demonstrated. Some numerical examples are provided to support our theoretical results and show the accuracy and efficiency of the proposed schemes.