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讨论了一类非线性中立型延迟积分微分方程Runge-Kutta方法的稳定性.在适当的条件下证明了运用Runge-Kutta方法求解这类方程既是数值稳定的也是渐近稳定的. 相似文献
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该文研究比例延迟微分方程组具有刚性精度变步长Runge-Kutta方法的渐近稳定性,给出了一类普遍意义下的变步长格式。证明当且仅当其稳定函数在无穷远点处的模小于1时,变步长Runge-Kutta方法渐近稳定。 相似文献
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一类重要的常微分方程源自用线方法求解非线性双曲型 偏微分方程,这类常微分方程的解具有单调性, 因此要求数值方法能保持原系统的这种性质.本文研究多步Runge-Kutta方法求解常微分方程初值问题的保单调性.分别获得了多步Runge-Kutta方法是条件单调和无条件单调的充分条件.
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本文讨论了一类Rosenbrock方法求解比例延迟微分方程,y′(t)=λy(t) μy(qt),λ,μ∈C,0 相似文献
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Stability Analysis of Runge-Kutta Methods for Non-Linear Delay Differential Equations 总被引:13,自引:0,他引:13
This paper is concerned with the numerical solution of delay differential equations(DDEs). We focus on the stability behaviour of Runge-Kutta methods for nonlinear DDEs. The new concepts of GR(l)-stability, GAR(l)-stability and weak GAR(l)-stability are further introduced. We investigate these stability properties for (k, l)-algebraically stable Runge-Kutta methods with a piecewise constant or linear interpolation procedure. 相似文献
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This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay.where $B,C,D\in C^{d\times d},q\in (0,1)$,and $B$ is regular. After transforming the above equation to non-automatic neutral equation with constant delay, we determine sufficient conditions for the asymptotic stability of the zero solution. Furthermore, we focus on the asymptotic stability behavior of Runge-Kutta method with variable stepsize. It is proved that a L-stable Runge-Kutta method can preserve the above-mentioned stability properties. 相似文献
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Cheng-jianZhang GengSun 《计算数学(英文版)》2004,22(3):447-456
In this paper, we deal with the boundedness and the asymptotic stability of linear and one-leg multistep methods for generalized pantograph equations of neutral type, which arise from some fields of engineering. Some criteria of the boundedness and the asymptotic stability for the methods are obtained. 相似文献
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K. J. In 't Hout 《BIT Numerical Mathematics》2001,41(2):322-344
This paper deals with the adaptation of Runge—Kutta methods to the numerical solution of nonstiff initial value problems for delay differential equations. We consider the interpolation procedure that was proposed in In 't Hout [8], and prove the new and positive result that for any given Runge—Kutta method its adaptation to delay differential equations by means of this interpolation procedure has an order of convergence equal to min {p,q}, where p denotes the order of consistency of the Runge—Kutta method and q is the number of support points of the interpolation procedure.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
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In this paper we discuss two-stage diagonally implicit stochastic Runge-Kutta methods with strong order 1.0 for strong solutions of Stratonovich stochastic differential equations. Five stochastic Runge-Kutta methods are presented in this paper. They are an explicit method with a large MS-stability region, a semi-implicit method with minimum principal error coefficients, a semi-implicit method with a large MS-stability region, an implicit method with minimum principal error coefficients and another implicit method. We also consider composite stochastic Runge-Kutta methods which are the combination of semi-implicit Runge-Kutta methods and implicit Runge-Kutta methods. Two composite methods are presented in this paper. Numerical results are reported to compare the convergence properties and stability properties of these stochastic Runge-Kutta methods. 相似文献
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This paper is devoted to a study of nonlinear stability of general linear methods for the numerical solution of delay differential equations in Hilbert spaces. New stability concepts are further introduced. The stability properties of (k,p,q)-algebraically stable general linear methods with piecewise constant or linear interpolation procedure are investigated. We also discuss stability of linear multistep methods viewed as a special subset of the class of general linear methods. 相似文献
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广义时滞微分方程的渐近稳定性和数值分析 总被引:3,自引:0,他引:3
考虑了广义时滞微分方程的初值问题,分析了用线性多步法求解一类广义滞后型微分系统数值解的稳定性,在一定的Lagrange插值条件下,给出并证明了求解广义滞后型微分系统的线性多步法数值稳定的充分必要条件。 相似文献
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本讨论非线性变延迟微分方程隐式Euler法的渐近稳定性。我们证明,在方程真解渐近稳定的条件下,隐式Euler法也是渐近稳定的。 相似文献
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该文涉及多延迟微分方程MDDEs系统的理论解与数值解的收缩性.为此,一些新的稳定性概念诸如:BN_f^(m)-稳定性及GRN_m-稳定性稳定性被引入.该探讨得出:Runge Kutta(RK)方法及相应的连续插值的BN^(m)-稳定性导致求解MDDEs的方法的收缩性(GRN_m-稳定性). 相似文献