共查询到19条相似文献,搜索用时 78 毫秒
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本文讨论多比例延迟微分方程的散逸性,给出了多比例延迟微分方程是散逸的充分条件,它可视为文献[8]中相应结果的推广。 相似文献
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考虑非线性中立型延迟积分微分方程数值方法的散逸性,把一类线性多步法应用到以上问题中,当积分项用复合求积公式逼近时,证明该数值方法在满足一定条件下具有散逸性. 相似文献
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研究一类积分微分方程线性多步方法(p,σ)的散逸性.当积分项用复合求积公式逼近时,证明了线性多步方法是有限维散逸的.这说明该方法很好地继承了系统本身所具有的重要性质.这一结论为数值求解这一类微分方程提供了更多的选择. 相似文献
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本文利用变分迭代法求解比例延迟微分方程。通过解一些比例延迟微分方程,说明变分迭代法能很好地得到比例延迟微分方程的解。 相似文献
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本文针对一类积分微分方程讨论Runge-Kutta方法的散逸性,当积分项用PQ公式逼近时,证明了(k,l)-代数稳定的Runge-Kutta方法是D(l)-散逸的. 相似文献
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本文利用三次样条配置方法采用直接法求解一类非线性分数阶比例延迟微分方程初值问题,并得到方法的局部截断误差.通过若干数值算例表明该方法求解分数阶比例延迟微分方程初值问题是非常有效的,本文的结果对于未来研究分数阶比例延迟微分方程的数值方法提供新的思路. 相似文献
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利用连续有限元法求解比例延迟微分方程,在一致网格下,给出比例延迟微分方程连续有限元解的整体收敛阶,数值实验验证了理论结果的正确性. 相似文献
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本文利用Jacobi配置方法数值求解几类分数阶多项比例延迟微分方程初值问题,给出相应的误差分析,并利用若干数值算例验证了相应的理论结果,表明Jacobi配置方法求解这几类分数阶比例延迟方程是高效的.同时,也为分数阶泛函微分方程的数值算法提供新的研究思路. 相似文献
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讨论了一类带分数Brown运动时变随机种群收获系统数值解的均方散逸性.在一定条件下,利用It公式和Bellman-Gronwall-Type引理,研究了方程(1)具有均方散逸性.分别利用带补偿的倒向Euler方法和分步倒向Euler方法讨论数值解的均方散逸性存在的充分条件,并通过数值算例对所给出的结论进行了验证. 相似文献
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This paper is concerned with the dissipativity of Volterra functional differential equations in a Hilbert space. A sufficient condition for dissipativity of one class of such equations is obtained. This result is applied to delay differential equations and integro-differential equations to obtain dissipativity results that are more general and deeper than related results in the previous literature. 相似文献
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Generalized Halanay inequalities for dissipativity of Volterra functional differential equations 总被引:1,自引:0,他引:1
Liping Wen Yuexin Yu Wansheng Wang 《Journal of Mathematical Analysis and Applications》2008,347(1):169-178
This paper is concerned with the dissipativity of theoretical solutions to nonlinear Volterra functional differential equations (VFDEs). At first, we give some generalizations of Halanay's inequality which play an important role in study of dissipativity and stability of differential equations. Then, by applying the generalization of Halanay's inequality, the dissipativity results of VFDEs are obtained, which provides unified theoretical foundation for the dissipativity analysis of systems in ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs), Volterra delay-integro-differential equations (VDIDEs) and VFDEs of other type which appear in practice. 相似文献
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This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations.We investigate the dissipativity properties of (k,l)algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid.The finitedimensional and infinite-dimensional dissipativity results of (k,l)-algebraically stable Runge-Kutta methods are obtained. 相似文献
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Liping Wen Wansheng Wang Yuexin Yu 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(3-4):1746-1754
This paper is concerned with the dissipativity and asymptotic stability of the theoretical solutions of a class of nonlinear neutral delay integro-differential equations (NDIDEs). We first give a generalization of the Halanay inequality which plays an important role in the study of dissipativity and stability of differential equations. Then, we apply the generalization of the Halanay inequality to NDIDEs and the dissipativity and the asymptotic stability results of the theoretical solution of NDIDEs are obtained. From a numerical point of view, it is important to study the potential of numerical methods in preserving the qualitative behavior of the analytical solutions. Therefore, the results, presented in this paper, provide the theoretical foundation for analyzing the dissipativity and the asymptotic stability of the numerical methods when they are applied to these systems. 相似文献
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This paper is concerned with the numerical dissipativity of nonlinear Volterra functional differential equations (VFDEs). We give some dissipativity results of Runge-Kutta methods when they are applied to VFDEs. These results provide unified theoretical foundation for the numerical dissipativity analysis of systems in ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs), Volterra delay integro-differential equations (VDIDEs) and VFDEs of other type which appear in practice. Numerical examples are given to confirm our theoretical results. 相似文献
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This paper is concerned with the numerical dissipativity of a class of nonlinear neutral delay integro-differential equations. The dissipativity results are obtained for algebraically stable Runge–Kutta methods when they are applied to above problems. 相似文献
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In this paper, the delay-dependent dissipativity of nonlinear delay differential equations is studied. A new dissipativity criterion is derived, which is less conservative than those in the existing literature in some cases, especially for equations with small delays. 相似文献
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Zhengwen Tu Liangwei Wang Zhongwei Zha Jigui Jian 《Communications in Nonlinear Science & Numerical Simulation》2013,18(9):2562-2570
In this paper, we study the global dissipativity of a class of BAM neural networks with both time-varying and unbound delays. Based on Lyapunov functions and inequality techniques, several algebraic criteria for the global dissipativity are obtained. And the linear matrix inequality (LMI) approach is exploited to establish sufficient easy-to-test conditions which are related to the derivative of delay for the global dissipativity. Meanwhile, the estimations of the positive invariant set, globally attractive set and globally exponential attractive set are given out. Finally, two examples are presented and analyzed to demonstrate our results. 相似文献