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961.
Lower bounds of eigenvalues of the biharmonic operators by the rectangular Morley element methods 下载免费PDF全文
In this article, we analyze the lower bound property of the discrete eigenvalues by the rectangular Morley elements of the biharmonic operators in both two dimension (2D) and three dimension (3D). The analysis relies on an identity for the errors of eigenvalues. We explore a refined property of the canonical interpolation operators and use it to analyze the key term in this identity. In particular, we show that such a term is of higher order for 2D, and is negative and of second order for 3D, which causes a main difficulty. To overcome it, we propose a novel decomposition of the first term in the aforementioned identity. Finally, we establish a saturation condition to show that the discrete eigenvalues are smaller than the exact ones. We present some numerical results to demonstrate the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1623–1644, 2015 相似文献
962.
设Ω是 Rn中的有界区域 ,其边界足够光滑 ,λk为双调和算子在自由边界条件下的第 k个本征值 ,利用变分原理及 Fourier变换 ,给出了本征值部分和 ∑kj=1λj的一个上界 ,该上界仅依赖于区域的体积 . 相似文献
963.
A. A. Abramov V. I. Ul’yanova L. F. Yukhno 《Computational Mathematics and Mathematical Physics》2007,47(5):791-796
A method for calculating eigenvalues of a nonlinear spectral problem for one class of linear differential algebraic equations is proposed under the assumption of an analytical dependence on spectral parameter of the matrices appearing in the system of equations and the matrices determining boundary conditions. 相似文献
964.
965.
1引言非均匀杆的轴向自由振动方程为其中L为杆的长度,A(x)为杆的横截面积,E(x)为弹性模量,ρ(x)是杆的密度.杆的主振动的一般形式为u(x,t)=u(x)sin(wt φ), (2)其中u(x)满足d/dx[E(x)A(x)du/dx] λρ(x)A(x)u=0,λ=ω2.(3) 相似文献
966.
利用矩阵的初等变换求方阵的特征值 总被引:1,自引:0,他引:1
高阶方阵的特征多项式以及特征值的求得,在计算上往往有一定的难度.本文首先从理论上分析了存在一个上三角矩阵或者下三角矩阵与一个方阵相似;接着,提出了相似变换的概念,分析了相似变换中初等矩阵的选择方法;然后指出了利用相似变换在求方阵的特征多项式以及特征值时的方法,并列举若干实例给予了说明. 相似文献
967.
M. -J. Huang 《Acta Mathematica Hungarica》2007,117(4):341-348
We establish several comparison results on the eigenvalue gap for vibrating strings with symmetric single-well densities or
symmetric double-well densities.
相似文献
968.
We present new algorithms that accelerate the bisection method for the symmetric tridiagonal eigenvalue problem. The algorithms
rely on some new techniques, including a new variant of Newton's iteration that reaches cubic convergence (right from the
start) to the well separated eigenvalues and can be further applied to acceleration of some other iterative processes, in
particular, of the divide-and-conquer methods for the symmetric tridiagonal eigenvalue problem.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
969.
Andrii Khrabustovskyi 《Mathematical Methods in the Applied Sciences》2009,32(16):2123-2137
We study the asymptotic behavior of the eigenvalues and the eigenfunctions of the Laplace–Beltrami operator on a Riemannian manifold Mε depending on a small parameter ε>0 and whose structure becomes complicated as ε→0. Under a few assumptions on scales of Mε we obtain the homogenized eigenvalue problem. In addition we study the behavior of the heat equation on Mε and investigate the large time behavior of the homogenized equation. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
970.
Jamshid Khorsandi Shahnawaz 《International Journal of Infrared and Millimeter Waves》2005,26(9):1317-1328
A novel realization of non-uniform semivectorial finite difference method for the analysis of semiconductor optical waveguides is presented. By using non-uniform mesh structure computer time is saved while the accuracy is maintained. Also, the accuracy of the results increased by balancing the coefficient matrix without increasing computation time. Calculation of all eigenvalues (real and complex) is enabled by the method. The results of the calculation are compared for uniform and non-uniform methods and for two different optical waveguides. It is indicated that accuracy of the result is mainly dependent on the mesh refinement near the material interfaces. It is also indicated that for small mesh size using non-uniform method is necessary while uniform method is useless due to huge computer time and memory needed. 相似文献