A LOW-REGULARITY FOURIER INTEGRATOR FOR THE DAVEY-STEWARTSON II SYSTEM WITH ALMOST MASS CONSERVATION  

作　　者：Cui NING Chenxi HAO Yaohong WANG 宁翠;郝晨曦;王耀宏(School of Financial Mathematics and Statistics,Guangdong University of Finance,Guangzhou 510521,China;Center for Applied Mathematics,Tianjin University,Tianjin 300072,China)

机构地区：[1]School of Financial Mathematics and Statistics,Guangdong University of Finance,Guangzhou 510521,China [2]Center for Applied Mathematics,Tianjin University,Tianjin 300072,China

出　　处：《Acta Mathematica Scientia》2024年第4期1536-1549,共14页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(11901120);supported by the NSFC(12171356);the Science and Technology Program of Guangzhou,China(2024A04J4027)。

摘　　要：In this work,we propose a low-regularity Fourier integrator with almost mass conservation to solve the Davey-StewartsonⅡsystem(hyperbolic-elliptic case).Arbitrary order mass convergence could be achieved by the suitable addition of correction terms,while keeping the first order accuracy in H~γ×H^(γ+1)for initial data in H^(γ+1)×H^(γ+1)withγ>1.The main theorem is that,up to some fixed time T,there exist constantsτ_(0)and C depending only on T and‖u‖_(L^(∞)((0,T);H^(γ+1)))such that,for any 0<τ≤τ_(0),we have that‖u(t_(n),·)-u^(n)‖H_γ≤C_(τ),‖v(t_(n),·)-v^(n)‖_(Hγ+1)≤C_(τ),where u^(n)and v^(n)denote the numerical solutions at t_(n)=nτ.Moreover,the mass of the numerical solution M(u^(n))satisfies that|M(u^(n))-M(u_0)|≤Cτ~5.

关 键 词：Davey-StewartsonⅡsystem low-regularity exponential integrator first order accuracy mass conservation 

分 类 号：O241.82[理学—计算数学]