共查询到19条相似文献,搜索用时 656 毫秒
1.
《数学年刊A辑(中文版)》2016,(1)
根据半驯服Euler法讨论了具有Markov调制的随机年龄结构种群系统的数值解.在非局部Lipschitz条件下,利用Burkholder-Davis-Gundy不等式、Ito公式和Gronwall引理,证明了半驯服Euler数值解不仅强收敛阶数为0.5,而且这种方法在时间步长一定的条件下有很好的均方指数稳定性.最后通过数值例子对所给的结论进行了验证. 相似文献
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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. 相似文献
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将高精度的Split-Step Backward Euler方法应用于随机固定资产模型,在Lipschitz条件下,利用离散半鞅收敛定理,建立了Split-Step Backward Euler方法对应的数值解的几乎必然指数稳定性的判定准则,并通过数值例子对所给的结论进行了验证. 相似文献
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介绍了一类与年龄相关的随机固定资产系统倒向Euler数值解法.漂移系数和扩散系数在单边Lipschitz条件和有界条件下,建立了随机固定资产系统倒向Euler数值解均方渐近有界性的判定准则.最后通过数值算例对结论进行了验证. 相似文献
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本文研究带Poisson跳和Markovian调制的中立型随机微分方程的数值解的收敛性质.用数值逼近方法求此微分方程的解,并证明了Euler近似解在此线性增长条件和全局Lipschitz条件更弱的条件下仍均方收敛于此方程的解析解. 相似文献
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《数学的实践与认识》2017,(17)
讨论了一类带分数Brown运动随机固定资产模型数值解的均方散逸性.在漂移系数和扩散系数满足单边Lipschitz条件和有界条件下,建立了随机固定资产模型补偿倒向Euler法数值解均方散逸性的判定准则.最后通过数值算例对结论进行了验证. 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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研究了一类带Markov状态转换的跳扩散方程的数值解的问题,为讨论这类方程精确解的数值计算问题,我们给出了一种基于Euler格式的方程解的跳适应算法,并在一定的条件下,证明了基于这种新的跳适应算法所得到的方程的数值解是收敛于它的精确解,同时还给出了数值解收敛到其精确解的收敛阶数.最后,本文通过两个例子说明了这种跳适应算法的计算有效性. 相似文献
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A. Yu. Veretennikov 《Probability Theory and Related Fields》2003,125(1):135-152
We establish sufficient conditions under which the rate function for the Euler approximation scheme for a solution of an SDE is close to that for an exact solution. 相似文献
12.
For stochastic differential equations (SDEs) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient, the classical explicit Euler scheme fails to converge strongly to the exact solution. Recently, an explicit strongly convergent numerical scheme, called the tamed Euler method, has been proposed in [8] for such SDEs. Motivated by their work, we here introduce a tamed version of the Milstein scheme for SDEs with commutative noise. The proposed method is also explicit and easily implementable, but achieves higher strong convergence order than the tamed Euler method does. In recovering the strong convergence order one of the new method, new difficulties arise and kind of a bootstrap argument is developed to overcome them. Finally, an illustrative example confirms the computational efficiency of the tamed Milstein method compared to the tamed Euler method. 相似文献
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In this article, we derive the exact rate of convergence of some approximation schemes associated to scalar stochastic differential
equations driven by a fractional Brownian motion with Hurst index H. We consider two cases. If H>1/2, the exact rate of convergence of the Euler scheme is determined. We show that the error of the Euler scheme converges
almost surely to a random variable, which in particular depends on the Malliavin derivative of the solution. This result extends
those contained in J. Complex. 22(4), 459–474, 2006 and C.R. Acad. Sci. Paris, Ser. I 340(8), 611–614, 2005. When 1/6<H<1/2, the exact rate of convergence of the Crank-Nicholson scheme is determined for a particular equation. Here we show convergence
in law of the error to a random variable, which depends on the solution of the equation and an independent Gaussian random
variable. 相似文献
14.
《Journal of Computational and Applied Mathematics》2005,173(2):211-237
In this paper, the authors propose a numerical method to compute the solution of a Cauchy problem with blow-up of the solution. The problem is split in two parts: a hyperbolic problem which is solved by using Hopf and Lax formula and a parabolic problem solved by a backward linearized Euler method in time and a finite element method in space. It is proved that the numerical solution blows up in a finite time as the exact solution and the support of the approximation of a self-similar solution remains bounded. The convergence of the scheme is obtained. 相似文献
15.
In this article, we study the convergence analysis for the initial and boundary value problem of parabolic equations on a disk with singular solutions. It is assumed that the exact solution performs singular properties that its derivatives go to infinity at the boundary of the disk. We propose a fully implicit time-stepping numerical scheme. A stretching polynomial-like function with a parameter is used to construct a local grid refinement. Over the nonuniform partition, we combine the Swartztrauber-Sweet scheme and the backward Euler method in spatial and temporal discretization, respectively. We carry out convergence analysis and analyze the effects of the parameter. It is shown that our numerical scheme is of first order accuracy for temporal discretization and of almost second order accuracy for spatial discretization. Numerical experiments are performed to illustrate our analysis results and show that there exists an optimal value for the parameter to obtain a best approximate solution. 相似文献
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Xu Yang & Weidong Zhao 《高等学校计算数学学报(英文版)》2021,14(4):1085-1109
This work investigates strong convergence of numerical schemes for nonlinear multiplicative noise driving stochastic partial differential equations under
some weaker conditions imposed on the coefficients avoiding the commonly used
global Lipschitz assumption in the literature. Space-time fully discrete scheme is
proposed, which is performed by the finite element method in space and the implicit
Euler method in time. Based on some technical lemmas including regularity properties for the exact solution of the considered problem, strong convergence analysis
with sharp convergence rates for the proposed fully discrete scheme is rigorously
established. 相似文献
18.
The determination of boundary conditions for the Euler equations of gas dynamics in a pipe with partially open pipe ends is considered. The boundary problem is formulated in terms of the exact solution of the Riemann problem and of the St. Venant equation for quasi-steady flow so that a pressure-driven calculation of boundary conditions is defined. The resulting set of equations is solved by a Newton scheme. The proposed algorithm is able to solve for all inflow and outflow situations including choked and supersonic flow.Received: August 7, 2002; revised: November 11, 2002 相似文献
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Morten Bjørhus 《BIT Numerical Mathematics》1995,35(2):291-296
In this note we prove convergence results, including error estimates, for the dynamic iteration scheme where the forward Euler and backward Euler method are used to compute the iterates. The proofs are interesting in that they are exact analogues of the proof for the continuous case, using discrete versions of Gronwall's inequality. 相似文献