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911.
This paper considers a class of fourth order nonlinear difference equations Δ2(r
n
Δ2(y
n
) + Δ2(r
n
,f(n,n
n
)=0,n ∈N(n
0) wheref(n, y) may be classified as superlinear, sublinear, strongly superlinear and strongly sublinear. In superlinear and sublinear cases,
necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions
with special asymptotic properties. In strongly superlinear and strongly sublinear cases, sufficient conditions are given
for all solutions to be oscillatory.
Partially Supported by the National Science Foundation of China 相似文献
912.
A numerical analysis is presented for the unsteady compressible laminar boundary layer driven by a compression or expansion wave. Approximate or series expansion methods have been used for the problems because of the characteristics of the governing equations, such as non-linearity, coupling with the thermal boundary layer equation and initial conditions. Here a transformation of the governing equations and the numerical linearization technique are introduced to deal with the difficulties. First, the governing equations are transformed for the initial conditions by Howarth and semisimilarity variables. These transformations reduce the number of independent variables from three to two and the governing equations from partial to ordinary differential equations at the initial point. Next, the numerical linearization technique is introduced for the non-linearity and the coupling with the thermal boundary layer equation. Because the non-linear terms are linearized without sacrifice of numerical accuracy, the solutions can be obtained without numerical iterations. Therefore the exact numerical solution, not approximate or series expansion, can be obtained. Compared with the approximate or series expansion method, this method is much improved. Results are compared with the series expansion solutions. 相似文献
913.
张建华 《浙江大学学报(理学版)》1991,18(4):363-370
本文给出了解三维Stokes方程的Q:/Q。有限元的梯度算子核的特征,证明了广义的LBD条件 相似文献
914.
A numerical method based on the boundary-fitted finite difference method (BFDM) is presented in this paper. The boundaries are external (the boundary of the physical domain) and internal (which corresponds to the fracture network). The difference between this approach and the usual one lies in the inclusion of discrete fractures in the volume that represents the porous medium. The numerical model has been used in the prediction of the flow pattern in several internationally recognized verification cases and applied to the solution of hypothetical problems of interest to us in the field of nuclear waste repository modelling. The results obtained show that the numerical approach considered gives accurate and reliable predictions of the hydrodynamics of fractured-porous media, thus justifying its use for the above-mentioned studies. 相似文献
915.
将离散的平均场Ising模型转换为连续的模型,给出了显式差分格式。利用有界延拓法,证明了差分解的收敛性与稳定性。最后通过数值例子说明了此格式的可信性。 相似文献
916.
Zhangxin Chen 《Numerical Methods for Partial Differential Equations》2006,22(2):317-360
In this article we study two families of multiscale methods for numerically solving elliptic homogenization problems. The recently developed multiscale finite element method [Hou and Wu, J Comp Phys 134 (1997), 169–189] captures the effect of microscales on macroscales through modification of finite element basis functions. Here we reformulate this method that captures the same effect through modification of bilinear forms in the finite element formulation. This new formulation is a general approach that can handle a large variety of differential problems and numerical methods. It can be easily extended to nonlinear problems and mixed finite element methods, for example. The latter extension is carried out in this article. The recently introduced heterogeneous multiscale method [Engquist and Engquist, Comm Math Sci 1 (2003), 87–132] is designed for efficient numerical solution of problems with multiscales and multiphysics. In the second part of this article, we study this method in mixed form (we call it the mixed heterogeneous multiscale method). We present a detailed analysis for stability and convergence of this new method. Estimates are obtained for the error between the homogenized and numerical multiscale solutions. Strategies for retrieving the microstructural information from the numerical solution are provided and analyzed. Relationship between the multiscale finite element and heterogeneous multiscale methods is discussed. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
917.
利用有限尺寸标度分析方法,研究了考虑次近邻相互作用的正方点阵完全阻挫XY模型的Ising型相变现象.结果表明对于次近邻耦合系数x=0.5的情况,系统存在Ising型相变,临界温度Tc=0.4043±0.0005,临界指数ν=0.80±0.05. 相似文献
918.
We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows. 相似文献
919.
本文研究快速扩散方程ut-Δum +| u|p =0的柯西问题 ,其中m ,p∈ ( 0 ,1) .对于 0
相似文献
920.
Zhu You-lan Chen Bin-mu Ren Hongliang Xu Hanping 《Advances in Computational Mathematics》2003,19(1-3):147-158
This paper is devoted to numerical methods for American barrier and lookback options, which are important examples of American exotic options. Since the singularity-separating method is adopted, accurate numerical results can be obtained very fast. 相似文献