A DISCRETE MODEL WITH INTERACTION BETWEEN THE BUDWORM AND ITS PREDATOR IN A CIRCULAR REGION

We consider a discrete model with interaction between the budworm and its predator in aeircular region. The number and properties of steady solutions, and the asymptotic behaviour ofunsteady solution are discussed.     

孤立波数值方法综述(Ⅰ)

This paper is devoted to introduce the history of numerical study of solitons and the main results for K. D. V. equation, R. L. W. equation, Klein-Gordon equation, Sine-Gordon equation and so on.The technique for constructing difference schemes based on conservation and characteristic is discussed. The two main methods for analysis of stability is given too. Then several finite element methods are discussed. The final part of this paper is for various-spectral methods.     

三维涡度方程的谱-差分方法(Ⅱ)

本文是[1]的继续。本文中建立了一些半离散函数空间中的嵌入定理及其它估计式,然后应用能量法严格估计了[1](高等学校计算数学学报,1991,13(2))中的谱一差分格式的广义稳定性,并在一定条件下推出收敛性。本文所采用的证明方法可应用于其它非线性偏微分方程局部方向周期问题的数值解法。     

论离散能量法(Ⅰ)

能量方法直接来源于守恒律。例如考虑一根两端固定的均匀细弦在空气中作阻尼运动,阻力与速度成正比,阻尼系数是b(x)≥0。用U(x,t)表示弦对平衡位置的偏移,那末它满足下列方程     

可压缩流动的Fourier谱-有限元解法

本文考虑n维(n=2,3)可压缩流动的带有单向周期边值条件问题的数值解.我们在周期方向采用Fourier谱方法,在非周期方向采用有限元方法,从而构造了一类谱-有限元格式.文中严格分析了计算误差,得到了收敛阶的估计.     

三维涡度方程单向周期初边值问题的拟谱─有限差分方法

本文对三维涡度方程单向周期初边值问题建立了一种Fourier拟谱-有限差分格式,分析了其广义稳定性和收敛性,数值结果显示了这种方法的优点。     

Spectral-finite element method for compressible fluid flow

In this paper, a combined Fourier spectral-finite element method is proposed for solving n-dimensional (n=2, 3), semi-periodio compressible fiuid flow problems. The strict error estimation as well as the convergence rate, is presented.     

LOCALIZATION AND APPROXIMATION OF ATTRACTORS FOR THE KURAMOTO-SIVASHINSKY EQUATIONS

1Intr0ducti0nThestudy0fglobalattrartorhasagreatdealtodowiththatofthelargetimebehavi0urofthesolutionsofdissipativepartialdtherentialequations.Usually,theattractoristypicallyacomplicated,fractalsubset0fthephasespace.Hellcetheconceptofinertialmallif0ld(IM),apositivelyinvariantfinite-dimensi0nalLipschitzmanifoldthatexponentiallyattractseveryorbit,wasdevelopedandithasbecomeakeytoolinthisareaofstudy.(See,e-g-,[l],[21andreferencestherein.)Themotivatingideabehindtheinertialmanif0ldist0embedtheattrac…     

应用广义Laguerre函数的Navier-Stokes方程外部问题混合谱方法

研究应用广义Laguerre函数的四阶非线性偏微分方程外部问题混合谱方法.构造了圆外Navier-Stokes方程流函数形式的混合谱方法,数值结果显示了该方法在空间方向的谱精度.     

NON-ISOTROPIC JACOBI SPECTRAL METHODS FOR UNBOUNDED DOMAINS

Some specific non-isotropic Jacobi approximations in multiple-dimensions are investigated, which are used for numerical solutions of differential equations on various unbounded domains. The convergence of proposed schemes are proved. Some efficient algorithms are provided. Numerical results are presented to illustrate the efficiency of this new approach.