二维Cahn-Hilliard方程半隐的预估-校正谱逼近(英文)

针对二维Cahn-Hilliard方程的初边值问题提出了一个便于计算的、半隐的预估-校正谱格式.通过引入两个三线性泛函,克服了非线性项所带来的困难,并用能量方法严格证明了数值解在时间方向具有二阶精度,而在空间方向具有谱精度.     

一类求解BURGERS方程的LEGENDRE谱格式

本文考虑非稳态Burgers方程的初边值问题,构造了一类Legendre谱计算格式,证明了其收敛性并给出了一些数值试验结果。     

长时间计算的二阶LEGENDRE谱格式(I)

本文提出了一类二阶Legendre谱格式,并考虑了反应扩散方程。证明了数值解的存在性和唯一性。模拟了原问题的守恒型和长时间性态。     

长时间计算的二阶LEGENDRE谱格式（Ⅰ）

本文提出了一类二阶Ｌｅｇｅｎｄｒｅ谱格式，并考虑了反应扩散方程，证明了数值解的存在性和唯一性，模拟了原问题的守恒型和长时间性态。     

Error estimation of prediction-correction legendre spectral approximation to incompressible fluid flow

1. IntroductionThere have been a lot of literatures concerning the existence, uniqueness, regularityof the solution of Navier-Stokes equation. Usually the primitive equation is considered,e.g.5 see 11,2]. Maily methods are used for its numerical simulation, e.g., see [2--7]. But wemeet several difficulties in calculation. For instance, if we use the finite difference method,then we have to evaluate the pressure at each time step. Some authors developed theartificial compressibility method or…     

THE PREDICTION-CORRECTION LEGENDRE SPECTRAL SCHEME FOR NONLINEAR EVOLUTIONARY PROBLEMS

The initial-boundary value problem of Burgers equation is considered. A prediction-correction Legendre spectral scheme is proposed. It possesses the accuracy of second order in time and higher order in space. The numerical experiments show the high accuracy of this approach.     

非线性发展型方程的Legendre拟谱逼近

本文考虑非稳态Burgers方程的拟谱逼近，构造了一类Legendre拟谱计算格式并证明了其收敛性，数值结果显示了格式的有效性。