隐式Euler法关于Volterra延迟积分方程的数值稳定性

本文涉及隐式Euler法应用于非线性Volterra型延迟积分方程的稳定性,其探讨了基于非经典Lipschitz条件,其方法的整体与渐近稳定性结果被获得。     

非线性变延迟微分方程隐式Euler方法的数值稳定性

在减弱对非线性刚性变延迟微分方程初值问题本身的约束条件的前提下 ,将已有的文献中隐式Euler方法数值稳定性的结论由常延迟的情形推广到了变延迟的情形 ,证明了隐式Euler方法是稳定的     

带分数布朗Brown的随机比例方程半隐式Euler法的数值解(英文)

本文给出并分析了Poisson随机跳测度驱动的带分数Brown运动的随机比例方程半隐式Euler法的数值解,在局部Lipschitz条件下,证明了在均方意义下半隐式Euler数值解收敛到精确解.     

渐近A稳定的线性多步法

本文主要结果为: 1.构造了一类k步k+1阶隐式线性多步公式,它们是渐近A稳定的。 2.构造了一类k步k阶隐式线性多步公式,它们是stiff稳定且是渐近A稳定的。 3.构造了一类k步k—1阶显式线性多步公式,它们是渐近A稳定的。k为任意正整数。     

与年龄相关的模糊随机种群系统的半隐式Euler法的收敛性

介绍了一类与年龄相关的模糊随机种群系统的半隐式Euler法.系统同时受到两种不确定性因素的影响:即,随机和模糊.在有界的条件(弱于线性增长条件)和Lipschitz条件下,讨论了与年龄相关的模糊随机种群系统在半隐式Euler法下的收敛性.方法具有克服线性计算不稳定的优点.最后通过例子对算法进行了验证.     

中立型随机比例延迟微分方程平衡半隐式Euler方法的均方收敛性

本文讨论求解刚性中立型随机比例延迟微分方程的平衡半隐式Euler方法。证明了中立型随机比例延迟微分方程的平衡半隐式Euler方法是1／2阶均方收敛的。     

延迟微分方程隐式Euler方法的收敛性

本文讨论了用隐式Euler方法求解一类延迟量满足Lipschitz条件且Lipschitz常数小于1的非线性变延迟微分方程初值问题的收敛性.获得了带线性插值的隐式Euler方法的收敛性结果.     

用线方法求解带混合边值条件的抛物方程

研制了分别用显式Euler法、隐式Euler法、Crank-Nicolson格式(梯形方法)求解带第一、第二及混合边值条件的抛物问题的应用软件,通过求解若干抛物问题对该软件作了测试,获得了预期的数值结果,讨论了时间和空间步长的变化对格式计算结果的影响,得到了三种方法的稳定性、收敛精度和计算量.     

两个带变时间步的两重网格算法的稳定性分析

对用于求解非线性发展方程的两个带变时间步的两重网格算法，对空间变量用有限元离散，对时间变量分别用一阶精度Euler显式和二阶精度半隐式差分格式离散，然后构造两重网格算法，通过深入的稳定性分析，得出本文的算法优于标准全离散有限元算法。     

无波动,无自由参数,耗散的隐式差分格式

本文建立了求解NS方程和Euler方程无波动、无自由参数、耗散的隐式差分格式.该格式是TVD的和无条件稳定的.其隐式部分在1,2,3维情况下仅分别依赖于3,5,9个点,且系数矩阵是主对角占优的.计算例题表明,该方法可获得和显式方法相同的精度,能很好地捕捉激波和剪切层,且计算时间比显式有较多的节省.     

Stability of Runge-Kutta methods for delay differential systems with multiple delays

The stability of Runge-Kutta methods for systems of delay differentialequations (DDEs) with multiple delays is considered. The stabilityregions of explicit and implicit Runge-Kutta methods are discussedwhen they are applied to asymptotically stable linear DDEs withmultiple delays. A simple estimate on the stability regionsof explicit Runge-Kutta methods is presented. It is shown thatthe stable step-size for numerical integration of DDEs withmultiple delays can be easily selected by means of the estimate.     

Delay-independent stability of Euler method for nonlinear one-dimensional diffusion equation with constant delay

This paper is concerned with delay-independent asymptotic stability of a numerical process that arises after discretization of a nonlinear one-dimensional diffusion equation with a constant delay by the Euler method. Explicit sufficient and necessary conditions for the Euler method to be asymptotically stable for all delays are derived. An additional restriction on spatial stepsize is required to preserve the asymptotic stability due to the presence of the delay. A numerical experiment is implemented to confirm the results.      

CONVERGENCE OF PARALLEL DIAGONAL ITERATION OF RUNGE-KUTTA METHODS FOR DELAY DIFFERENTIAL EQUATIONS

Implicit Runge-Kutta method is highly accurate and stable for stiff initial value prob-lem.But the iteration technique used to solve implicit Runge-Kutta method requires lotsof computational efforts.In this paper,we extend the Parallel Diagonal Iterated Runge-Kutta(PDIRK)methods to delay differential equations(DDEs).We give the convergenceregion of PDIRK methods,and analyze the speed of convergence in three parts for theP-stability region of the Runge-Kutta corrector method.Finally,we analysis the speed-upfactor through a numerical experiment.The results show that the PDIRK methods toDDEs are efficient.     

Variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff DDE solver of order 4 to 14

This article presents a solver for delay differential equations (DDEs) called HBO414DDE based on a hybrid variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff ODE solver of order 4 to 14. The current version of our method solves DDEs with state dependent, non-vanishing, small, vanishing and asymptotically vanishing delays, except neutral type and initial value DDEs. Delayed values are computed using Hermite interpolation, small delays are dealt with by extrapolation, and discontinuities are located by a bisection method. HBO414DDE was tested on several problems and results were compared with those of known solvers like SYSDEL and the recent Matlab DDE solver ddesd and statistics show that it gives, most of the time, a smaller relative error than the other solvers for the same number of function evaluations.     

Asymptotic behavior of multistep runge-kutta methods for systems of delay differential equations

1. IntroductionIn order to assess the asymptotic behavior of numerical methods for DDEs, much attention has been given in the literature to the scalar case (cL [1-6]). UP to now) only partialresults (of. [7-10]) have dealt with the delay systemswhere y(t) = (yi(t), so(t),' ) yp(t))" E Cd, which is unknown for t > 0, L and M areconstat complex p x Hmatrices, T > 0 is a constat delay and W(t) 6 CP is a specifiedinitial function.In [111, C.J. Zhang and S.Z. Zhou made an investigation on…     

Stability of Runge-Kutta methods for linear delay differential equations

Summary. This paper investigates the stability of Runge-Kutta methods when they are applied to the complex linear scalar delay differential equation . This kind of stability is called stability. We give a characterization of stable Runge-Kutta methods and then we prove that implicit Euler method is stable. Received November 3, 1998 / Revised version received March 23, 1999 / Published online July 12, 2000     

The Numerical Stability of the $\theta$-Method for Delay Differential Equations with Many Variable Delays

This paper deals with the asymptotic stability of theoretical solutions and numerical methods for the delay differential equations (DDEs)where $a, b_1, b_2, ... b_m$ and $y_0 \in C, 0 < \lambda_m \le \lambda_{m-1} \le ... \le \lambda_1<1$. A sufficient condition such that the differential equations are asymptotically stable is derived. And it is shown that the linear $\theta$-method is $\bigwedge GP_m$-stable if and only if$\frac{1}{2}\le \theta \le 1$.     

单物种人口模型指数隐式Euler方法的振动性

本文研究了用以描述单物种人口模型的延迟Logistic方程的数值振动性.对方程应用隐式Euler方法进行求解,针对离散格式定义了指数隐式Euler方法,证明了该方法的收敛阶为1.根据线性振动性理论获得了数值解振动的充分条件.进而还对非振动数值解的性质作了讨论.最后用数值算例对理论结果进行了验证.