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21.
We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point. 相似文献
22.
许明浩 《武汉大学学报(理学版)》1996,(1)
讨论如下Hilbert空间中的半线性随机发展方程的Cauchy问题 dy(t)=[Ay(t) f(t,y(t))]dt G(t,y(t))dw(t) y(O)=V_u的适度解的存在唯一性,在更一般的条件下,得到了该问题的适度解的存在唯一性。 相似文献
23.
本文给出了混合型多项式Hammerstein积分方程正解的迭代求法,并将所得结果应用到二阶非线性常微分方程的边值问题 相似文献
24.
Stability of chirped bright and dark soliton-like solutions of the cubic complex Ginzburg-Landau equation with variable coefficients 总被引:1,自引:0,他引:1
Fang Fang 《Optics Communications》2006,268(2):305-310
We consider an inhomogeneous optical fiber system described by the generalized cubic complex Ginzburg-Landau (CGL) equation with varying dispersion, nonlinearity, gain (loss), nonlinear gain (absorption) and the effect of spectral limitation. Exact chirped bright and dark soliton-like solutions of the CGL equation were found by using a suitable ansatz. Furthermore, we analyze the features of the solitons and consider the problem of stability of these soliton-like solutions under finite initial perturbations. It is shown by extensive numerical simulations that both bright and dark soliton-like solutions are stable in an inhomogeneous fiber system. Finally, the interaction between two chirped bright and dark soliton-like pulses is investigated numerically. 相似文献
25.
An Improved Gradient Projection-based Decomposition Technique for Support Vector Machines 总被引:2,自引:0,他引:2
Luca Zanni 《Computational Management Science》2006,3(2):131-145
In this paper we propose some improvements to a recent decomposition technique for the large quadratic program arising in
training support vector machines. As standard decomposition approaches, the technique we consider is based on the idea to
optimize, at each iteration, a subset of the variables through the solution of a quadratic programming subproblem. The innovative
features of this approach consist in using a very effective gradient projection method for the inner subproblems and a special
rule for selecting the variables to be optimized at each step. These features allow to obtain promising performance by decomposing
the problem into few large subproblems instead of many small subproblems as usually done by other decomposition schemes. We
improve this technique by introducing a new inner solver and a simple strategy for reducing the computational cost of each
iteration. We evaluate the effectiveness of these improvements by solving large-scale benchmark problems and by comparison
with a widely used decomposition package. 相似文献
26.
JI Li-Na QU Chang-Zheng 《理论物理通讯》2006,46(10)
The present paper discusses a class of nonlinear diffusion-convection equations with source. The method that we use is the conditional symmetry method. It is shown that the equation admits certain conditional symmetries for coefficient functions of the equations. As a consequence, solutions to the resulting equations are obtained. 相似文献
27.
28.
Volker Elling. 《Mathematics of Computation》2006,75(256):1721-1733
A particular case of initial data for the two-dimensional Euler equations is studied numerically. The results show that the Godunov method does not always converge to the physical solution, at least not on feasible grids. Moreover, they suggest that entropy solutions (in the weak entropy inequality sense) are not well posed.
29.
30.
分析光场与高聚物相互作用的微观机制,介绍高分子与小分子在光场作用下的极化过程。对在窄束光场作用下,高分子链极化后链上各处极化程度的分布情况进行研究,指出对于高度拉伸的聚合物薄膜,电偶极子模型不适合准确解释高分子与光场相互作用的微观机制。为此,采用符合实际的天线模型分析高分子天线与窄束光场的相互作用,从理论上推导出天线模型高分子链上一小段的极化公式,并用离散变分方法——DVM(discrete variational method)计算一个高分子链的极化分布,验证了文中推导出的分式的合理性。最后,将极化分布看作是电流在天线上的分布,计算了天线的次级辐射在空间中的角分布,得到天线模型对电偶极子模型的修正因子。 相似文献