共查询到20条相似文献,搜索用时 156 毫秒
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随机延迟微分方程的全隐式Euler方法 总被引:1,自引:0,他引:1
研究随机延迟微分方程数值解具有重要的意义,目前已有显式和半隐式两种数值方法,还没有全隐式的数值方法.本文构造了一种全隐式Euler方法,在该方法中用一些截断的随机变量代替维纳过程增量△W<,n>,接着证明了全隐式方法是1/2阶收敛的并通过数值实验验证了该方法的收敛性.最后,用数值实验表明在某些情况下全隐式方法的稳定性比半隐式方法好一些. 相似文献
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给出了线性分段连续型随机微分方程指数Euler方法的均方指数稳定性.经典的对稳定性理论分析,通常应用的是Lyapunov泛函理论,然而,应用该方程本身的特点和矩阵范数的定义给出了该方程精确解的均方稳定性.以往对于该方程应用隐式Euler方法得到对于任意步长数值解的均方稳定性,而应用显式Euler方法得到了相同的结果.最... 相似文献
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本文研究高度非线性随机微分方程(SDEs)的数值解稳定性性质.给出θ-方法均方指数稳定性的充分条件.与现有文献不同,本文无需单边线性增长条件和充分小的步长.本文在单调型的条件下,并且至于要步长满足一个很弱的条件即可.因此本文是对现有文献的很大改进. 相似文献
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本文主要研究了非线性随机Pantograph微分方程,讨论了其零解的均方渐近稳定性并给出了零解均方渐近稳定的充分条件.在本文的第三部分,我们将随机θ-方法应用于这类问题,获得了数值解均方渐近稳定条件. 相似文献
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本文讨论Milstein方法用于求解线性中立型随机延迟微分方程初值问题时数值解的稳定性,给出了Milstein方法均方稳定的一个充分条件.文末的数值试验证实了本文所获理论结果的正确性. 相似文献
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本文讨论Euler方法用于求解线性中立型随机延迟微分方程初值问题时数值解的稳定性,利用了一种不同于以往文献中的证明技巧,给出了Euler方法均方稳定的一个充分条件.文末的数值试验证实了本文所获理论结果的正确性. 相似文献
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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、It\^{o} 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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Guo-Feng Zhang 《计算数学(英文版)》2003,21(3):375-382
Consider the following neutral delay-differential equations with multiple delays (NMDDE)$$y'(t)=Ly(t)+\sum_{j=1}^{m}[M_jy(t-\tau_j)+N_jy'(t-\tau_j)],\ \ t\geq 0, (0.1)$$ where $\tau>0$, $L, M_j$ and $N_j$ are constant complex- value $d×d$ matrices. A sufficient condition for the asymptotic stability of NMDDE system (0.1) is given. The stability of Butcher's (A,B,C)-method for systems of NMDDE is studied. In addition, we present a parallel diagonally-implicit iteration RK (PDIRK) methods (NPDIRK) for systems of NMDDE, which is easier to be implemented than fully implicit RK methos. We also investigate the stability of a special class of NPDIRK methods by analyzing their stability behaviors of the solutions of (0.1). 相似文献
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The stability of small perturbations against a constant background is studied for a system of quasi-gasdynamic equations in an arbitrary number of space variables. It is established that, for a fixed adiabatic exponent γ, the stability is determined only by the background Mach number, and a necessary and sufficient condition for stability at any Mach number is $\gamma \leqslant \bar \gamma $ , where $\bar \gamma \approx 6.2479$ . The proof is based on a direct analysis of the corresponding complex characteristic numbers depending on several parameters. The multidimensional case is successfully reduced to the one-dimensional one. Then, the generalized Routh-Hurwitz criterion is applied in conjunction with analytical calculations based on Mathematica. 相似文献
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Solutions to the $\sigma_k$-Loewner-Nirenberg Problem on Annuli are Locally Lipschitz and Not Differentiable 下载免费PDF全文
Yanyan Li & Luc Nguyen 《数学研究》2021,54(2):123-141
We show for $k \geq 2$ that the locally Lipschitz viscosity solution to the $\sigma_k$-Loewner-Nirenberg problem on a given annulus $\{a < |x| < b\}$ is $C^{1,\frac{1}{k}}_{\rm loc}$ in each of $\{a < |x| \leq \sqrt{ab}\}$ and $\{\sqrt{ab} \leq |x| < b\}$ and has a jump in radial derivative across $|x| = \sqrt{ab}$. Furthermore, the solution is not $C^{1,\gamma}_{\rm loc}$ for any $\gamma > \frac{1}{k}$. Optimal regularity for solutions to the $\sigma_k$-Yamabe problem on annuli with finite constant boundary values is also established. 相似文献
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In this paper, we discuss a fixed point theorem for mappings derived by a pair of mappings satisfying weak(k, k/) contractive type condition on the tensor product spaces. Let X and Y be Banach spaces and T_1 : X γ Y → X and T_2: X γ Y → Y be two operators which satisfy weak(k, k/) contractive type condition. Using T_1 and T_2, we construct an operator T on X γ Y and show that T has a unique fixed point in a closed and bounded subset of X γ Y.We derive an iteration scheme converging to this unique fixed point of T. Conversely, using a weakly contractive mapping T, we construct a pair of mappings(T_1, T_2) satisfying weak(k, k/)contractive type condition on X γ Y and from this pair, we also obtain two self mappings S_1 and S_2 on X and Y respectively with unique fixed points. 相似文献
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Consider initial value probiom v_t-u_x=0, u_t+p(v)_x=0, (E), v(x, 0)=v_0(x), u(x, 0)=u_0(x), (I), where A≥0, p(v)=K~2v~(-γ), K>0, 0<γ<3. As 0<γ≤1, the authors give a sufficient condition for that (E), (I) to have a unique global smooth solution, As 1≤γ<3, a necessary condition is given for that. 相似文献
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In this paper, we mainly study the scattering operators for a Poincaré-Einstein manifold $(X^{n+1}, g_+)$, which define the fractional GJMS operators $P_{2\gamma}$ of order $2\gamma$ for $0<\gamma<\frac{n}{2}$ for the conformal infinity $(M, [g])$. We generalise Guillarmou-Qing's positivity results in [8] to the higher order case. Namely, if $(X^{n+1}, g_+)$ $(n\geq 5)$ is a hyperbolic Poincaré-Einstein manifold and there exists a smooth representative $g$ for the conformal infinity such that the scalar curvature $R_g$ is a positive constant and $Q_4$ is semi-positive on $(M, g)$, then $P_{2\gamma}$ is positive for $\gamma\in [1,2]$ and the first real scattering pole is less than $\frac{n}{2}-2$. 相似文献
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假设a,b0并且K_(a,b)(x)=(e~(i|x|~(-b)))/(|x|~(n+a))定义强奇异卷积算子T如下:Tf(x)=(K_(a,b)*f)(x),本文主要考虑了如上定义的算子T在Wiener共合空间W(FL~p,L~q)(R~n)上的有界性.另一方面,设α,β0并且γ(t)=|t|~k或γ(t)=sgn(t)|t|~k.利用振荡积分估计,本文还研究了算子T_(α,β)f(x,y)=p.v∫_(-1)~1f(x-t,y-γ(t))(e~(2πi|t|~(-β)))/(t|t|~α)dt及其推广形式∧_(α,β)f(x,y,z)=∫_(Q~2)f(x-t,y-s,z-t~ks~j)e~(-2πit)~(-β_1_s-β_2)t~(-α_1-1)s~(-α_2-1)dtds在Wiener共合空间W(FL~p,L~q)上的映射性质.本文的结论足以表明,Wiener共合空间是Lebesgue空间的一个很好的替代. 相似文献
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Evans functions and bifurcations of standing wave fronts of
a nonlinear system of reaction diffusion equations 下载免费PDF全文
Linghai Zhang 《Journal of Applied Analysis & Computation》2016,6(2):515-530
Consider the following nonlinear system of reaction diffusion equations arising from mathematical neuroscience
$\frac{\partial u}{\partial t}=\frac{\partial^2u}{\partial x^2}+\alpha[\beta H(u-\theta)-u]-w,~
\frac{\partial w}{\partial t}=\varepsilon(u-\gamma w).$
Also consider the nonlinear scalar reaction diffusion equation $\frac{\partial u}{\partial t}=\frac{\partial^2u}{\partial x^2}+\alpha[\beta H(u-\theta)-u].$
In these model equations, $\alpha>0$, $\beta>0$, $\gamma>0$, $\varepsilon>0$ and $\theta>0$ are positive constants, such that $0<2\theta<\beta$.
In the model equations, $u=u(x,t)$ represents the membrane potential of a neuron at position $x$ and time $t$,
$w=w(x,t)$ represents the leaking current, a slow process that controls the excitation.\\indent The main purpose of this paper is to couple together linearized stability criterion (the equivalence of the nonlinear stability, the linear stability and the spectral stability of the standing wave fronts) and Evans functions (complex analytic functions)
to establish the existence, stability, instability and bifurcations of standing wave fronts of the nonlinear system of reaction diffusion equations
and to establish the existence and stability of the standing wave fronts of the nonlinear scalar reaction diffusion equation. 相似文献
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We show that in $\operatorname{PG}(4,2)$ there exist octets $\mathcal{P}
_{8}=\{\pi_{1},\,\ldots\,,\pi_{8}\}$ of planes such that the 28
intersections $\pi_{i}\cap\pi_{j}$ are distinct points. Such
conclaves (see [6]) $\mathcal{P}_{8}$ of planes
in $\operatorname{PG}(4,2)$ are shown to be in bijective correspondence
with those planes $P$ in $\operatorname{PG}(9,2)$ which are external to
the Grassmannian $\mathcal{G}_{1,4,2}$ and which belong to the orbit
$\operatorname{orb}(2\gamma)$ (see [4]). The fact
that, under the action of $\operatorname{GL}(5,2),$ the stabilizer
groups $\mathcal{G}_{\mathcal{P}_{8}}$ and $\mathcal{G}_{P}$ both have
the structure $2^{3}:(7:3)$ is thus illuminated. Starting out from a
regulus-free partial spread $\mathcal{S}_{8}$ in
$\operatorname{PG}(4,2)$ we also give a construction of a conclave of
planes $P\in\operatorname{orb}(2\gamma)\subset\operatorname{PG}(9,2).$ 相似文献