共查询到19条相似文献,搜索用时 187 毫秒
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非线性计算不稳定问题的进一步研究 总被引:1,自引:3,他引:1
讨论了有关非线性计算不稳定的若干问题,其主要内容有(1)考察了有代表性的三类发展方程,指出其对应的差分格式是否出现非线性计算不稳定,与原微分方程解的性质密切相关;(2)进一步讨论了带周期边条件的守恒型差分格式的非线性计算稳定性问题,总结了克服非线性不稳定的有效措施;(3)以非线性平流方程为例,着重分析了带非周期边条件的非守恒差分格式的非线性计算稳定性问题,给出了判别其计算稳定性的"综合分析判别法". 相似文献
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强迫耗散非线性发展方程显式差分格式的计算稳定性 总被引:1,自引:1,他引:1
基于计算准稳定的概念来分析强迫耗散非线性发展方程显式差分格式的计算稳定性,给出强迫耗散非线性大气方程组显式差分格式计算准稳定的判据,为设计强迫耗散非线性大气方程组计算稳定的显式差分格式提供了新的思路和理论依据 相似文献
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利用有限差分方法研究了一类非线性Cahn-Hilliard方程,为方程建立了一种三层有限差分格式,讨论了差分解的收敛性和稳定性.虽然格式建立的是一次O(h)边界条件,但是由△2U的定义,可以得到误差次数为O(h2+k2). 相似文献
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本文讨论了一类具有时滞的差分方程的渐近稳定性。利用矩阵性质和不等式技巧给出了该类方程渐近稳定的充要条件。 相似文献
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本文首先证明了布尔减、布尔除与非运算构成完备集,并根据布尔减、布尔除与非运算的运算规则和性质,从与或非代数系统中的最小项、最大项展开式出发,推导了任意逻辑函数在减除非代数系统中的标准DOS(减之除)和标准SOD(除之减)展开式。最后举例说明了二个代数系统中展开式之间的转换。本文的工作对进一步完善布尔代数的四则运算理论具有一定的意义。 相似文献
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泥石流是一种介于崩塌滑坡和洪水之间的物理过程,既有土体的结构性,又有水体的流动性。随着泥石流运动控制方程和数值模拟技术的发展,基于数值模拟的泥石流危险性分区方法成为泥石流危险性分区的主要方法。本文应用Massflow模型,基于深度平均的连续介质力学方法,从Navier-Stokes方程出发,推导出二维运动堆积控制方程,采用MacCormack-TVD有限差分算法计算,根据古交官长沟的地形条件、水文条件、物源条件模拟了泥石流运动的全过程,计算得出泥石流泛滥范围内的流深和流速。并根据数值模拟结果和最大动能分区模型,获取该流域的泛滥范围并确定危险性分区,将模拟区划分为四个区域,即高危险区、中危险区、低危险区和安全区。泥石流的分区模型是每个网格上泥石流体的最大动能,能够直接反应泥石流对建筑物的破坏能力,分区模型具有直接的物理意义。 相似文献
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This paper investigates the pth moment exponential stability of impulsive stochastic functional differential equations. Some sufficient conditions are obtained to ensure the pth moment exponential stability of the equilibrium solution by the Razumikhin method and Lyapunov functions. Based on these results, we further discuss the pth moment exponential stability of generalized impulsive delay stochastic differential equations and stochastic Hopfield neural networks with multiple time-varying delays from the impulsive control point of view. The results derived in this paper improve and generalize some recent works reported in the literature. Moreover, we see that impulses do contribute to the stability of stochastic functional differential equations. Finally, two numerical examples are provided to demonstrate the efficiency of the results obtained. 相似文献
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Yu Zhang 《Journal of The Franklin Institute》2011,348(8):1965-1982
In this paper, the robust exponential stability of uncertain impulsive delay difference equations is investigated. First, some robust exponential stability criteria for uncertain impulsive delay difference equations with continuous time in which the state variables on the impulses may relate to the time-varying delays are provided. Then a robust exponential stability result for uncertain linear impulsive delay difference equations with discrete time is given. Some examples, including an example which cannot be studied by the existing results, are also presented to illustrate the effectiveness of the obtained results. 相似文献
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In this paper, we are concerned with the analytical and numerical stability of nonlinear neutral delay integro-differential equations (NDIDEs). First, sufficient conditions for the analytical stability of nonlinear NDIDEs with a variable delay are derived. Then, we show that any A-stable linear multistep method can preserve the asymptotic stability of the analytical solution for nonlinear NDIDEs with a constant delay. At last, we validate our conclusions by numerical experiments. 相似文献
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A Chebyshev collocation method, an expansion method, has been proposed in order to solve the systems of higher-order linear integro-differential equations. This method transforms the IDE system and the given conditions into the matrix equations via Chebyshev collocation points. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Chebyshev coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method. Moreover, this method is valid for the systems of differential and integral equations. 相似文献
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Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects 总被引:1,自引:0,他引:1
In this paper, we study stability of a class of stochastic differential delay equations with nonlinear impulsive effects. First, we establish the equivalent relation between the stability of this class of stochastic differential delay equations with impulsive effects and that of a corresponding stochastic differential delay equations without impulses. Then, some sufficient conditions ensuring various stabilities of the stochastic differential delay equations with impulsive effects are obtained. Finally, two examples are also discussed to illustrate the efficiency of the obtained results. 相似文献
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A numerical method is proposed for solving multi-dimensional hyperbolic–parabolic differential equations with the nonlocal boundary condition in t and Dirichlet and Neumann conditions in space variables. The first and second order of accuracy difference schemes are presented. The stability estimates for the solution and its first and second orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolic–parabolic differential equations with variable coefficients in x and two-dimensional hyperbolic–parabolic equation. 相似文献
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《Journal of The Franklin Institute》2021,358(18):9890-9908
This paper aims at establishing necessary and sufficient conditions of exponential stability for linear discrete-time systems with multiple delays. Firstly, we introduce a new concept—Lyapunov matrix, and investigate its properties, existence and uniqueness by: (i) characterizing the solution of a boundary value problem of matrix difference equations; and (ii) constructing complete type Lyapunov–Krasovskii functionals with pre-specified forward difference. Secondly, a new constructive analysis methodology, named Lyapunov matrix approach, is proposed to establish necessary and sufficient exponential stability conditions for discrete-time systems with multiple delays. Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical results. It is worth emphasizing that, from a view of computation, the Lyapunov matrix approach proposed here is concerned with three key steps: (i) solve a systems of linear equations; (ii) check whether a constant matrix is of full-column-rank, and (iii) judge whether a constant matrix is positive definite. All of these can be easily realized by using the tool software—MATLAB. 相似文献
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There are few techniques available to numerically solve linear Fredholm integrodifferential-difference equation of high-order. In this paper we show that the Taylor matrix method is a very effective tool in numerically solving such problems. This method transforms the equation and the given conditions into the matrix equations. By merging these results, a new matrix equation which corresponds to a system of linear algebraic equation is obtained. The solution of this system yields the Taylor coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method. Moreover, this method is valid for the differential, difference, differential-difference and Fredholm integral equations. In some numerical examples, MAPLE modules are designed for the purpose of testing and using the method. 相似文献
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章德海 《中国科学院研究生院学报》2000,(2)
通过定义平移算子和差分算子 ,并利用Lax配对的方法 ,找到了KP差分 -微分方程组的正确形式 .定义了差分指数函数 .借助穿衣算子法 ,得到了KP差分 -微分方程组的精确解析解 .还讨论了KP差分 -微分方程组及其解的展开形式 . 相似文献