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41.
Two different problems are proposed as approximations of the usual system modelling natural convection under the Oberbeck-Boussinesq assumptions. The error is evaluated by means of the norm of its gradient in the Hilbert space. The average Nusselt number is also estimated. 相似文献
42.
In general, we will use the numerical differentiation when dealing with the differential equations. Thus the differential equations can be transformed into algebraic equations and then we can get the numerical solutions. But as we all have known, the numerical differentiation process is very sensitive to even a small level of errors. In contrast it is expected that on average the numerical integration process is much less sensitive to errors. In this paper, based on the Sinc method we provide a new method using Sinc method incorporated with the double exponential transformation based on the interpolation of the highest derivatives (SIHD) for the differential equations. The error in the approximation of the solution is shown to converge at an exponential rate. The numerical results show that compared with the exiting results, our method is of high accuracy, of good convergence with little computational efforts. It is easy to treat nonhomogeneous mixed boundary condition for our method, which is unlike the traditional Sinc method. 相似文献
43.
Jing-na Li Xiao-feng Wang Zheng-an Yao 《应用数学学报(英文版)》2007,23(3):421-432
In this paper, we propose a model in studying soft ferromagnetic films, which is readily accessible experimentally. By using penalty approximation and compensated compactness, we prove that the dynamical equation in thin film has a local weak solution. Moreover, the corresponding linear equation is also dealt with in great detail. 相似文献
44.
B. V. Pal’tsev I. I. Chechel’ 《Computational Mathematics and Mathematical Physics》2006,46(5):820-847
The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 103. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ~ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ~ 5 × 103. 相似文献
45.
Mark A. S. Aarons 《Calculus of Variations and Partial Differential Equations》2006,25(2):205-246
We study the forced mean curvature flow of graphs in Minkowski space and prove longtime existence of solutions. When the forcing
term is a constant, we prove convergence to either a constant mean curvature hypersurface or a translating soliton – depending
on the boundary conditions at infinity.
It is a pleasure to thank my PhD advisors Klaus Ecker and Gerhard Huisken for their assistance and encouragement. I also thank
Maria Athanassenas, Oliver Schnürrer and Marty Ross for their interest and useful comments, and the Max Planck Gesellschaft
for financial support. 相似文献
46.
47.
Arne Barinka Stephan Dahlke Wolfgang Dahmen 《Advances in Computational Mathematics》2006,24(1-4):5-34
Recently adaptive wavelet methods have been developed which can be shown to exhibit an asymptotically optimal accuracy/work
balance for a wide class of variational problems including classical elliptic boundary value problems, boundary integral equations
as well as certain classes of noncoercive problems such as saddle point problems. A core ingredient of these schemes is the
approximate application of the involved operators in standard wavelet representation. Optimal computational complexity could
be shown under the assumption that the entries in properly compressed standard representations are known or computable in
average at unit cost. In this paper we propose concrete computational strategies and show under which circumstances this assumption
is justified in the context of elliptic boundary value problems.
Dedicated to Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 41A25, 41A46, 65F99, 65N12, 65N55.
This work has been supported in part by the Deutsche Forschungsgemeinschaft SFB 401, the first and third author are supported
in part by the European Community's Human Potential Programme under contract HPRN-CT-202-00286 (BREAKING COMPLEXITY). The
second author acknowledges the financial support provided through the European Union's Human Potential Programme, under contract
HPRN-CT-2002-00285 (HASSIP) and through DFG grant DA 360/4–1. 相似文献
48.
We have generalized the coherent potential approximation (CPA) of Tripathi and Behera to the case of ann-component alloy. It is seen that then-component CPA density of states reproduces the binary, ternary quartenary alloys etc when the appropriate limits are adopted. 相似文献
49.
对称正交反对称矩阵反问题解存在的条件 总被引:25,自引:1,他引:24
戴华 《高等学校计算数学学报》2002,24(2):169-178
矩阵反问题和矩阵特征值反问题在科学和工程技术中具有广泛的应用,有关它们的研究已取得了许多进展[1,2].[3]和[4]分别研究了反对称矩阵反问题和双反对称矩阵特征值反问题等.本文研究一类更广泛的对称正交反对称矩阵反问题.用Rn×m(Cn×m)表示n×m实(复)矩阵的全体,ASRn×n表示n阶反对称矩阵的全体,ABSRn×n表示n阶双反对称矩阵的全体,ORn×n表示n阶正交矩阵的全体.A+表示矩阵A的Moore-Penrose广义逆.In表示n阶单位矩阵.ei表示n阶单位矩阵的第i列,Sn=[en,en-1, 相似文献
50.
Roland Opfer 《Advances in Computational Mathematics》2006,25(4):357-380
This paper reconstructs multivariate functions from scattered data by a new multiscale technique. The reconstruction uses
standard methods of interpolation by positive definite reproducing kernels in Hilbert spaces. But it adopts techniques from
wavelet theory and shift-invariant spaces to construct a new class of kernels as multiscale superpositions of shifts and scales
of a single compactly supported function φ. This means that the advantages of scaled regular grids are used to construct the
kernels, while the advantages of unrestricted scattered data interpolation are maintained after the kernels are constructed.
Using such a multiscale kernel, the reconstruction method interpolates at given scattered data. No manipulations of the data
(e.g., thinning or separation into subsets of certain scales) are needed. Then, the multiscale structure of the kernel allows
to represent the interpolant on regular grids on all scales involved, with cheap evaluation due to the compact support of
the function φ, and with a recursive evaluation technique if φ is chosen to be refinable. There also is a wavelet-like data
reduction effect, if a suitable thresholding strategy is applied to the coefficients of the interpolant when represented over
a scaled grid. Various numerical examples are presented, illustrating the multiresolution and data compression effects. 相似文献