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991.
Zheng-su Wan Ben-yu Guo Zhong-qing Wang 《计算数学(英文版)》2006,24(4):481-500
In this paper, we investigate Jacobi pseudospectral method for fourth order problems. We establish some basic results on the Jacobi-Gauss-type interpolations in non-uniformly weighted Sobolev spaces, which serve as important tools in analysis of numerical quadratures, and numerical methods of differential and integral equations. Then we propose Jacobi pseudospectral schemes for several singular problems and multiple-dimensional problems of fourth order. Numerical results demonstrate the spectral accuracy of these schemes, and coincide well with theoretical analysis. 相似文献
992.
Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields
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Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields. 相似文献
993.
In this paper, we propose an adaptive defect-correction method for natural convection (NC) equations. A defect-correction method (DCM) is proposed for solving NC equations to overcome the convection dominance problem caused by a high Rayleigh number. To solve the large amount of computation and the discontinuity of the gradient of the numerical solution, we combine a new recovery-type posteriori estimator in view of the gradient recovery and superconvergent theory. The presented reliability and efficiency analysis shows that the true error can be effectively bounded by the recovery-based error estimator. Finally, the stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations. 相似文献
994.
ZHANG Shun-Li 《理论物理通讯》2006,45(6):969-978
The generalized conditional symmetry is developed to study the variable
separation for equations of type uxt=A(u,ux)uxx+B(u,ux). Complete classification of those equations which admit derivative-dependent functional separable solutions is obtained and some of their
exact separable solutions are constructed. 相似文献
995.
In the present paper the Lie symmetrical non-Noether conserved
quantity of the Poincaré-Chetaev equations of a generalized
classical mechanics under the general infinitesimal transformations
of Lie groups is discussed. First, we establish the determining
equations of Lie symmetry of the equations. Second, the Lie symmetrical
non-Noether conserved quantity of the equations is deduced. Finally,
an example is given to illustrate the application of the results. 相似文献
996.
LIU Hong-Zhun PAN Zu-Liang LI Peng 《理论物理通讯》2006,46(10)
In this article, we will derive an equality, where the Taylor series expansion around ε = 0for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted.By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-B(a)cklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-B(a)cklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples. 相似文献
997.
利用拟合实测的TEMP Ⅱ型加速器磁绝缘二极管(MID)电压波形及其焦点附近束流密度曲线,建立了Gaussian分布模型,据此计算了与靶作用的离子的能量及数量,采用Monte Carlo(MC)方法计算了沉积在靶内的能量.并以此作为热源,与流体动力学(HD)模型相结合,对不同的靶状态采用相应的状态方程,模拟计算了靶内压力演化情况; 同时对烧蚀产生的等离子体采用理想气体状态方程, 结合HD方程组, 模拟计算了喷发过程中压力的空间演化过程.
关键词:
强流脉冲离子束
Gaussian模型
HD方程
数值研究 相似文献
998.
999.
X射线光栅微分相衬成像对由轻元素构成的物质的内部探测具有传统吸收成像无法比拟的优势, 尤其在癌症的早期诊断和轻元素材料及器件的无损检测等领域应用潜力巨大. 大视场成像是影响该技术从实验室走向实际应用的重要因素. 针对大视场成像的客观需求, 基于菲涅耳衍射原理和光栅结构特征, 建立了量化物理模型用于分析影响成像视场的因素, 提出了实现大成像视场的有效途径, 为未来大视场光栅微分相衬成像方法的设计和应用提供理论依据. 相似文献
1000.
Differential scanning calorimetry (DSC) and x-ray diffraction (XRD) are employed to investigate the effects of nickel on the crystallization of the amorphous Zr70Cu20Ni10 alloy. We have found that the crystallization process of the amorphous Zr70Cu20Ni10 alloy is strongly influenced by the addition of nickel. Addition of 10 at% Ni to the Zr70Cu30 amorphous alloy makes the crystallization process proceed from a single-stage mode to a double-stage mode. The activation energy for crystallization of the amorphous Zr70Cu20Ni10 alloy is calculated to be about 388kJ·mol-1 on the basis of the Kissinger equation. The effects of nickel on the crystallization of the amorphous Zr70Cu20Ni10 alloy are discussed in terms of the genetics of metals. 相似文献