共查询到16条相似文献,搜索用时 359 毫秒
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蔡好涛 《数学物理学报(A辑)》2006,26(3):421-425
该文首先给出Cauchy型主值积分φ(wf,x)的一种求积公式φm*(wf,x),然后证明序列$φm*(wf,x)}m=2∞在整个闭区间[-1,1]上是一致收敛到Cauchy型主值积分φ(wf,x)的,同时给出它的误差界. 相似文献
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在该文中, 令E表示一个迭代函数系统(X,T1,…, Tm). 的吸引子. 定义连续自映射 f : E→E为f(x)=T-1j(x), x∈ Tj(E), j=1, …, m . 给定Given ψ ∈CR(E), 令
Kψ(δ, n = sup{∣∑n-1k=0[ψ(f kx)-ψ(f ky)]|:y ∈ Bx (δ, n)},
这里Bx(δ, n) 表示Bowen球. 取一个扩张常数 ε, 记Kψ=supn Kψ(ε, n) , 定义ν(E)={ψ : Kψ < ∞}. 对f : E → E, 作为Ruelle的一个定理[3, 定理2.1]的一个应用, 我们证明每个ψ ∈ν(E)具有惟一的平衡态. 此结果推广了文献[12]中的主要结果. 相似文献
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研究集值映射方程0 T (z)的求解问题, 其中T是极大单调算子.对于给定的xk及β k>0, 大部分已有的近似邻近点算法取xk+1= 满足 xk +ek +βkT(xk ), ||ek||≤hk||xk- xk ||, 其中{hk}为非负可加数列. 新方法中不取 xk+1 = xk , 而将新的迭代点取为 xk+1 = PΩ [xk-ek], 其中Ω 是T的定义域,PΩ (8729;) 表示Ω上的投影算子. 在supk>0hk < 1这样宽松的条件下给出了收敛性证明. 相似文献
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对二阶非线性椭圆型方程∑ i,j=1n Di[Aij(x)Djy]+∑i=1n bi(x)Diy+q(x)f(y)=e(x)建立了若干新的振动准则, 所得结果仅依赖于方程在外区域Ω С Rn的一个子区域序列的信息而有别于已知的大多数结论. 相似文献
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一类修正的Navier-Stokes方程的长时间性态 总被引:3,自引:0,他引:3
该文主要讨论,Rn上一类修正的 Navier-Stokes 方程弱解的长时间性态, 通过进一步改进Fourier分解方法, 得到了当初速度u0∈ L2 ∩L1时其弱解在L2 范数下的最优衰减率为 (1+t)n/4 同时该文也给出了修正的Navier-Stokes 方程与经典Navier-Stokes 方程的误差估计. 相似文献
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该文利用变分方法讨论了方程 -△p u=λa(x)(u+)p-1-μa(x)(u-)p-1+f(x, u), u∈W01,p(\Omega)在(λ, μ)\not\in ∑p和(λ, μ) ∈ ∑p 两种情况下的可解性, 其中\Omega是 RN(N≥3)中的有界光滑区域, ∑p为方程 -△p u=α a(x)(u+)p-1-βa(x)(u-)p-1, u∈ W01,p(\Omega)的Fucik谱, 权重函数a(x)∈ Lr(\Omega) (r≥ N/p)$且a(x)>0 a.e.于\Omega, f满足一定的条件. 相似文献
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该文讨论了偶数阶边值问题 (-1)m y(2m)=f(t,y), 0≤t≤1,ai+1y(2i) (0)-βi+1y (2i+1) (0)=0, γi+1y(2i) (1)+δi+1y(2i+1) (1)=0,0≤i ≤m-1正解的存在性.借助于Leggett-Williams 不动点定理,建立了该问题存在三个及任意奇数个正解的充分条件. 相似文献
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该文研究了线性微分方程L(f)=f(k)+Ak-1(z)f(k-1)+ … +A0(z)f=F(z) (k∈ N)的复振荡理论, 其中系数Aj(z) (j=0, … , k-1)和F(z)是单位圆△={z:|z|<1}内的解析函数. 作者得到了几个关于微分方程解的超级, 零点的超收敛指数以及不动点的精确估计的定理. 相似文献
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We study a preconditioner for the h-p version of the boundaryelement method for hypersingular integral equations in threedimensions. The preconditioner is based on a three-level decompositionof the underlying ansatz space, the levels being piecewise bilinearfunctions on a coarse grid, piecewise bilinear functions ona fine grid, and piecewise polynomials of high degree on thefine grid. We prove that the condition number of the preconditionedlinear system is bounded by maxj (1 + log Hjpj/hj)2 where Hjis the diameter of an element j of the coarse grid, hj is thesize of the elements of the fine grid on j, and pj is the maximumof the polynomial degrees used in j. Numerical results supportingour theory are reported.
Received 9 March 1999. Accepted 19 July 1999. 相似文献
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Highly-oscillatory integrals are allegedly difficult to calculate.The main assertion of this paper is that that impression isincorrect. As long as appropriate quadrature methods are used,their accuracy increases when oscillation becomes faster andsuitable choice of quadrature points renders this welcome phenomenonmore pronounced. We focus our analysis on Filon-type quadratureand analyse its behaviour in a range of frequency regimes forintegrals of the form 0h f(x)ei x w(x)d x, where h>0 issmall and | | large. Our analysis is applied to modified Magnus methods for highly-oscillatoryordinary differential equations.
Received 6 June 2003. Revised 14 October 2003. 相似文献
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We study the numerical solution procedure for two-dimensional Laplace’s equation subjecting to non-linear boundary conditions.
Based on the potential theory, the problem can be converted into a nonlinear boundary integral equations. Mechanical quadrature
methods are presented for solving the equations, which possess high accuracy order O(h
3) and low computing complexities. Moreover, the algorithms of the mechanical quadrature methods are simple without any integration
computation. Harnessing the asymptotical compact theory and Stepleman theorem, an asymptotic expansion of the errors with
odd powers is shown. Based on the asymptotic expansion, the h
3 −Richardson extrapolation algorithms are used and the accuracy order is improved to O(h
5). The efficiency of the algorithms is illustrated by numerical examples. 相似文献
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On the Local and Superlinear Convergence of Quasi-Newton Methods 总被引:13,自引:0,他引:13
BROYDEN C. G.; DENNIS J. E. Jr.; MOR? JORGE J. 《IMA Journal of Applied Mathematics》1973,12(3):223-245
This paper presents a local convergence analysis for severalwell-known quasi-Newton methods when used, without line searches,in an iteration of the form
to solve for x* such that Fx* = 0. The basic idea behind theproofs is that under certain reasonable conditions on xo, Fand xo, the errors in the sequence of approximations {Hk} toF'(x*)1 can be shown to be of bounded deterioration inthat these errors, while not ensured to decrease, can increaseonly in a controlled way. Despite the fact that Hk is not shownto approach F'(x*)1, the methods considered, includingthose based on the single-rank Broyden and double-rank Davidon-Fletcher-Powellformulae, generate locally Q-superlinearly convergent sequences{xk}. 相似文献
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Let MS be the universal maximal operator over unit vectors ofarbitrary directions. This operator is not bounded in L2(R2).We consider a sequence of operators over sets of finite equidistributeddirections converging to MS. We provide a new proof of N. Katz'sbound for such operators. As a corollary, we deduce that MSis bounded from some subsets of L2 to L2. These subsets arecomposed of positive functions whose Fourier transforms havea logarithmic decay or which are supported on a disc. 1991 MathematicsSubject Classification 42B25. 相似文献
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Mechanical quadrature methods and their extrapolation for solving first kind Abel integral equations
This paper presents high accuracy mechanical quadrature methods for solving first kind Abel integral equations. To avoid the ill-posedness of problem, the first kind Abel integral equation is transformed to the second kind Volterra integral equation with a continuous kernel and a smooth right-hand side term expressed by weakly singular integrals. By using periodization method and modified trapezoidal integration rule, not only high accuracy approximation of the kernel and the right-hand side term can be easily computed, but also two quadrature algorithms for solving first kind Abel integral equations are proposed, which have the high accuracy O(h2) and asymptotic expansion of the errors. Then by means of Richardson extrapolation, an approximation with higher accuracy order O(h3) is obtained. Moreover, an a posteriori error estimate for the algorithms is derived. Some numerical results show the efficiency of our methods. 相似文献