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1.
三维抛物型方程的一个新的高精度显式差分格式   总被引:4,自引:0,他引:4  
本文建立解三维抛物型方程的一个新的高精度三层显式差分格式,其稳定性条件为,而截断误差为  相似文献   

2.
本文研究二阶变系数线性双曲型方程初边值问题某些交替方向差分格式的稳定性与收敛性,所用方法是建立差分格式之解的能量不等式。  相似文献   

3.
张天德  王玮 《工科数学》1998,14(3):11-16
对于热传导方程构造了两个高阶精度的差分格式,一个是三层七点显格式.另一个是三层九点隐格式.证明了差分格式的收敛性和稳定性,最后给出数值计算结果。  相似文献   

4.
对于热传导方程构造了两个高阶精度的差分格式,一个是三层七点显格式,另一个是三层九点隐格式.证明了差分格式的收敛性和稳定性,最后给出数值计算结果.  相似文献   

5.
张关泉 《计算数学》1982,4(3):298-312
序言 用差分方程逼近常微分方程边值问题,或用隐式差分格式逼近演化型偏微分方程初边值问题时,通常需求解差分方程的两点边值问题.常用的方法是“追赶法”.在[1—4]中,讨论了各种类型的“追赶”法及其稳定性.在这些文章中,或依据系数矩阵特征值的性质,或依据差分方程两点边值问题在C模意义下的性态,来证明“追赶”法的稳定性.关于差分  相似文献   

6.
本文讨论一般的方程系数满足Lipschitz条件的变系数线性双曲型初边值问题差分格式的稳定性,并在很弱的条件下证明了几类差分格式是稳定的,本文还证明了:如果格式稳定,则在解和方程的系数足够光滑时,差分解将收敛于微分方程的解,并且g阶格式在l_2空间有g阶收敛速度。  相似文献   

7.
吴宏伟 《计算数学》2009,31(2):137-150
广义KPP(Kolmogorov-Petrovskii-Piskunov)方程是一个积分微分方程.为了要研究其数值解,我们首先将该方程转化为一个非线性双曲型方程,然后构造了一个线性化的差分格式,得到了差分格式解的存在唯一性,利用能量不等式证明了差分格式二阶收敛性和关于初值的无条件稳定性,数值结果验证了本文提出的方法.  相似文献   

8.
对广义Rosenau-KdV方程提出一种在时间层和空间层上分别具有二阶和四阶精度的三层线性差分格式,所建格式是离散质量守恒和离散能量守恒的,利用离散能量法证明了差分格式的可解性、收敛性和稳定性.数值实验验证了该格式的精度和守恒性.  相似文献   

9.
解对流方程的大多数常见的显式差分格式 ,其稳定性条件是苛刻的 .这一困难可由在常规的显式差分格式中引入耗散项而得到克服 .基于此 ,我们导出一类新的无条件稳定的两层的半显式差分格式及若干具有高稳定性的显式格式 .它们包含了若干已知的具有高稳定性的显式格式 .  相似文献   

10.
二维半线性反应扩散方程的交替方向隐格式   总被引:2,自引:0,他引:2  
吴宏伟 《计算数学》2008,30(4):349-360
本文研究一类二维半线性反应扩散方程的差分方法.构造了一个二层线性化交替方向隐格式.利用离散能量估计方法证明了差分格式解的存在唯一性、差分格式在离散H~1模下的二阶收敛性和稳定性.最后给出两个数值例子验证了理论分析结果.  相似文献   

11.
In this paper, we study the structural stability of solutions to the Riemann problem for one-dimensional isentropic Chaplygin gas. We perturb the Riemann initial data by taking three piecewise constant states and construct the global structure. By letting the perturbed parameter εε tend to zero, we prove that the Riemann solutions are stable under the local small perturbations of the Riemann initial data even when the initial perturbed density depending on the parameter but with no mass concentration limit.  相似文献   

12.
We analyze the well-posedness of the initial value problem for the generalized micropolar fluid system in a space of tempered distributions and also prove the existence of the stationary solutions. The asymptotic stability of solutions is showed in this space, and as a consequence, a criterium for vanishing small perturbations of initial data (stationary solution) at large time is obtained. A fast decay of the solutions is obtained when we assume more regularity on the initial data.  相似文献   

13.
The equations of flow in porous media attributable to Forchheimer are considered. In particular, the problem of thermal convection in such a medium is addressed when the viscosity varies with temperature. It is shown that nonlinear stability may be achieved naturally for all initial data by working with L 3 or L 4 norms. It is also shown that L 2 theory is not sufficient for such unconditional stability. Previous work has established nonlinear stability for vanishingly small initial data thresholds, but we believe this is the first analysis that addresses the important physical problem of unconditional stability. It is shown how to extend the nonlinear analysis for a viscosity linear in temperature to the cases when the viscosity may be quadratic or when penetrative convection is allowed in the layer.  相似文献   

14.
In this paper, we consider a nonlinear viscoelastic inverse problem with memory in the boundary. Under some suitable conditions on the coefficients, relaxation function, and initial data, we proved stability of solutions when the integral overdetermination tends to zero as time goes to infinity. Furthermore, we show that there are solutions under some conditions on initial data that blow up in finite time. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

15.
The system of equations describing the shallow‐water limit dynamics of the interface between two layers of immiscible fluids of different densities is formulated. The flow is bounded by horizontal top and bottom walls. The resulting equations are of mixed type: hyperbolic when the shear is weak and the behavior of the system is internal‐wave like, and elliptic for strong shear. This ellipticity, or ill‐posedness is shown to be a manifestation of large‐scale shear instability. This paper gives sharp nonlinear stability conditions for this nonlinear system of equations. For initial data that are initially hyperbolic, two different types of evolution may occur: the system may remain hyperbolic up to internal wave breaking, or it may become elliptic prior to wave breaking. Using simple waves that give a priori bounds on the solutions, we are able to characterize the condition preventing the second behavior, thus providing a long‐time well‐posedness, or nonlinear stability result. Our formulation also provides a systematic way to pass to the Boussinesq limit, whereby the density differences affect buoyancy but not momentum, and to recover the result that shear instability cannot occur from hyperbolic initial data in that case.  相似文献   

16.
In the previous paper(see Li and Zhu(2014)), for a characteristic problem with not necessarily small initial data given on a complete null cone decaying like that in the work of the stability of Minkowski spacetime by Christodoulou and Klainerman(1993), we proved the local existence in retarded time, which means the solution to the vacuum Einstein equations exists in a uniform future neighborhood, while the global existence in retarded time is the weak cosmic censorship conjecture. In this paper, we prove that the local existence in retarded time still holds when the data is assumed to decay slower, like that in Bieri's work(2007)on the extension to the stability of Minkowski spacetime. Such decay guarantees the existence of the limit of the Hawking mass on the initial null cone, when approaching to infinity, in an optimal way.  相似文献   

17.
UNIFORMSTABILITYANDASYMPTOTICBEHAVIOROFSOLUTIONSOF2-DIMENSIONALMAGNETOHYDRODYNAMICSEQUATIONSZHANGLINGHAIManuscriptreceivedJu...  相似文献   

18.
The aim of this paper is to study the structural stability of solutions to the Riemann problem for a scalar conservation law with a linear flux function involving discontinuous coefficients. It is proved that the Riemann solution is possibly instable when one of the Riemann initial data is at the vacuum. Furthermore, we point out that the Riemann solution is also possibly instable even when the Riemann initial data stay far away from vacuum. In order to deal with it, we perturb the Riemann initial data by taking three piecewise constant states and then the global structures and large time asymptotic behaviors of the solutions are obtained constructively. It is also proved that the Riemann solutions are unstable in some certain situations under the local small perturbations of the Riemann initial data by letting the perturbed parameter ε tend to zero. In addition, the interaction of the delta standing wave and the contact vacuum state is considered which appear in the Riemann solutions.  相似文献   

19.
We consider the Kirchhoff plate equation and the Bernoulli–Euler plate equation. The energy decay rate in both cases is investigated. Moreover, when we do not have exponential stability in the energy space, we give explicit logarithmic decay estimates valid for regular initial data. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

20.
We consider the problem of the long-time stability of plane waves under nonlinear perturbations of linear Klein-Gordon equations. This problem reduces to studying the distribution of the mode energies along solutions of one-dimensional semilinear Klein–Gordon equations with periodic boundary conditions when the initial data are small and concentrated in one Fourier mode. It is shown that for all except finitely many values of the mass parameter, the energy remains essentially localized in the initial Fourier mode over time scales that are much longer than predicted by standard perturbation theory. The mode energies decay geometrically with the mode number with a rate that is proportional to the total energy. The result is proved using modulated Fourier expansions in time.  相似文献   

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