共查询到18条相似文献，搜索用时 180 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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固体中冲击波及其一维一阶非线性演化方程数值模拟 总被引：1，自引：0，他引：1
定义固体中的冲击波为冲击波阵面及其后状态物理量发生急剧变化的狭窄区域。利用前人讨论结果进一步探讨了 4种边界输入形式下的冲击波形成距离计算式。分别采用具有二阶精度的显式MacCormack差分格式和MacCormackTVD格式对黏弹性、热弹性以及非均匀性非线性固体介质中一维一阶非线性演化方程进行数值模拟研究,探讨了这些复杂介质中冲击波的形成及演化的基本性质,并较成功地避免了非物理解的产生 相似文献
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以波传播的观点 ,将流动工况视为连续波与动力波相互作用在特定流动条件下的非线性解 ,尝试提出了两相流分析的一种新思路 .从一维气液两相流守恒方程出发 ,应用气液两相流漂移流模型 ,推导了空泡率双曲型守恒方程 ,用特征线法数值求解气液两相流空泡率分布的传播过程 ,对传播稳定性和流型转变进行讨论 .数值分析表明 ,低空泡率时发生流型转变的位置相对于两相流平均速度将向下游蔓延 ;而高空泡率时则相对地向上游蔓延 ;空泡率很高时空泡率分布传播过程中将不会出现流型转变 .计算表明 :流型转变起始点的空泡率为 0 2 7,空泡率达到 0 5 8时流型转变终止 ;这与文献报告的气液两相流实验结果符合较好 相似文献
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王斌 《中国科学院研究生院学报》1988,(2)
本文用待定系数法构造一类平方守恒型差分格式,使得国内外一些常用的在非交错格网上实现的平方守恒型格式均可作为其特例推导出来。此外,还讨论了构造显式完全平方守恒型差分格式的问题。 相似文献
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本文介绍了经典的线性声学理论与非线性声学理论以及一种非经典的非线性声学理论即基于接触作用的非线性声学理论.通过数值方法验证了接触非线性声学理论对于定量评价材料内部裂纹形态及损伤程度的可行性,并将数值试验结果的正确性进行了简要对比. 相似文献
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以球面正压浅水方程显式能量守恒格式的设计为例,在不失动力学方程物理意义的情况下,给出南北极网格点上速度的表达式,以及其预报方程的差分格式.克服数学意义上的极点奇异问题,直接预报极点速度.数值试验表明,此方法简单易行,能合理描述极点速度及其变化. 相似文献
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几种高精度差分格式的比较试验 总被引：1，自引：0，他引：1
具体比较了三种含基架网点少的高精度格式：紧致平方守恒格式、特征保形格式和特征Ｈｅｒｍｉｔｅ插值格式．实例表明前两种格式计算效果较好,第三种格式有明显位相差． 相似文献
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Sreten B. Stojanovic 《Journal of The Franklin Institute》2017,354(11):4549-4572
The problem of finite-time stability (FTS) for discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties is considered in this paper. In order to obtain less conservative stability criteria, a finite sum inequality with delayed states is proposed. Some sufficient conditions of FTS are derived in the form of the linear matrix inequalities (LMIs) by using Lyapunov–Krasovskii-like functional (LKLF) with power function and single/double summation terms. More precisely estimations of the upper bound of the initial value of LKLF and the lower bound of LKLF are proposed. As special cases, the FTS of nominal discrete-time systems with constant or time-varying delay is considered. The numerical examples are presented to illustrate the effectiveness of the results and their improvement over the existing literature. 相似文献
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《Journal of The Franklin Institute》2023,360(3):1690-1705
This paper proposes an extended generalized integral inequality based on free matrices (EGIIFM) and applies it to the stability analysis of neural networks with time-varying delays. The EGIIFM estimates an upper bound for a quadratic form of a positive definite matrix with an augmented vector staked not only with the state and its derivative but also with the nonlinear activation function. By reflecting the correlated cross-information among the terms in the augmented vector as free matrices, the EGIIFM provides a tighter upper bound and encompasses various existing single integral inequalities as special cases. In addition, by establishing a new double integral Lyapunov–Krasovskii functional including the correlated cross-information, a less conservative stability criterion is obtained. Through three well-known numerical examples, the effectiveness of the EGIIFM is evaluated. 相似文献
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动力保守系统的一类双属性格式 总被引：1，自引：1，他引：1
在动力保守系统的统一框架下,利用一种特殊变换,具体构造了一类在大气海洋问题中更具应用前景的差分格式,它们既满足平方守恒性,又是辛格式,不妨简称为双属性格式. 相似文献
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We propose a novel form of nonlinear stochastic filtering based on an iterative evaluation of a Kalman-like gain matrix computed within a Monte Carlo scheme as suggested by the form of the parent equation of nonlinear filtering (Kushner–Stratonovich equation) and retains the simplicity of implementation of an ensemble Kalman filter (EnKF). The numerical results, presently obtained via EnKF-like simulations with or without a reduced-rank unscented transformation, clearly indicate remarkably superior filter convergence and accuracy vis-à-vis most available filtering schemes and eminent applicability of the methods to higher dimensional dynamic system identification problems of engineering interest. 相似文献
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Xiucheng Shi Jianquan Lu Yang Liu Tingwen Huang Fuad E. Alssadi 《Journal of The Franklin Institute》2018,355(12):5256-5271
In this paper, we study the fixed-time consensus problem for multi-agent systems with structurally balanced signed graph. A new class of fixed-time nonlinear consensus protocols is designed by employing the neighbor’s information. By using Lyapunov stability method, states of all agents can be guaranteed to reach agreement in a fixed time under our presented protocols, and the consensus values are the same in modulus but different in sign. Moreover, it is shown that the settling time is not dependent on the initial conditions, and it makes a good convenience to estimate the convergence time by just knowing the graph topology and the information flow of the multi-agent systems. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed consensus protocols. 相似文献
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《Journal of The Franklin Institute》2022,359(17):9971-9988
The stability issue of discrete-time switched systems governed by cyclic switching laws is discussed in this paper. By establishing inverse-timer-based multiple Lyapunov functions (ITBMLFs), which are less conservative than traditional MLFs, limitations of the existing findings on discrete-time cyclic switched systems (DTCSSs) are well relaxed. Furthermore, from the perspective of computational complexity adjustment, the proposed ITBMLFs are confirmed to be more flexible than the previous ones, which is especially meaningful for the DTCSSs consisting of a large number of subsystems. Based on the cycle-dependent average dwell time (CD-ADT) concept and the ITBMLF approach, newly enhanced stability conditions are launched for DTCSSs where subsystems can be entirely or partially stable, or even completely unstable. Moreover, robust stability of DTCSSs can be achieved when norm-bounded and time-varying parameter uncertainties (NBTVPUs) are taken into account. Finally, the effectiveness and superiority of the proposed technologies are expounded through numerical examples. 相似文献