共查询到19条相似文献,搜索用时 256 毫秒
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本文介绍了分段均值有界变差函数(PMBVF)的定义,分别给出了正弦与余弦积分一致收敛性的充分必要条件. 相似文献
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一类奇异积分方程组的样条间接近似解法 总被引:3,自引:0,他引:3
本文利用三次复插值样条函数给了定义于复平面上光滑封闭曲线上的一类奇异积分方程组(1)的一种间接近似解法,讨论了误差估计和一致收敛性。 相似文献
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周育人 《数学物理学报(A辑)》1995,15(3):241-249
本文给出了带Hilbert核奇异积分的几种数值求积分式,证明了它们的一致收敛性,把它们应用于常系数带Hilbert核的奇异积分方程可获得的逼近解,而且在输入函数晚一般的假定下,证明了这些解的唯一存在性收敛性。 相似文献
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本文采用三次Birkhoff型插值样条讨论任意光滑弧上的奇异积分T_w(f:x,r)=∫_p(w(t)f(t))/(t-x)dt的逼近,在f(t)∈D_1,权函数w(t)∈D_1.分划序列拟一致的条件下,证明了其一致收敛性. 相似文献
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半直线上的Hammerstein积分方程的有限截段逼近 总被引:3,自引:0,他引:3
在半直线上线性积分方程:的数值求解中,用方程(0.1)相应的有限截段方程的解、x_m(s)逼近原方程的解x(s)的方法得到x_m对x在有限区间上的一致收敛性结果.用这种方法研究方程(0.1)的数值解日见增多,特别是在[1]中,Anselone与Sloan提出所谓点列的“严格收敛性”概念来研究方程(0.1)与(0.2)的关系,显著地改 相似文献
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王小林 《数学物理学报(A辑)》1997,17(3):348-355
利用复插值样条函数,给出了定义于光滑封闭曲线上一般的正则型奇异积分方程的样条间接逼近解法,证明了一致收敛性.对于其中的一类奇异积分方程,还给出了近似解和误差估计. 相似文献
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函数列的一致收敛性与所讨论的区间有关.在区间的子区间或不同的区间上,函数列的一致收敛性表现如何呢?通过几个命题和几个实例,并利用几何画板可以帮助我们辨别函数列在不同区间上的一致收敛性. 相似文献
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利用函数列的极限理论方法,研究函数列积分极限中积分和极限可交换次序的问题.对一致收敛的可积函数列给出积分的极限定理,对一致有界局部一致收敛函数列给出积分控制收敛定理,通过大量实例表明该理论的意义所在. 相似文献
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We show that generalized approximation spaces can be used to prove stability and convergence of projection methods for certain types of operator equations in which unbounded operators occur. Besides the convergence, we also get orders of convergence by this approach, even in case of non-uniformly bounded projections. We give an example in which weighted uniform convergence of the collocation method for an easy Cauchy singular integral equation is studied. 相似文献
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Gennadi Vainikko 《Numerical Functional Analysis & Optimization》2013,34(3):313-338
We study the convergence and convergence speed of two versions of spline collocation methods on the uniform grids for linear Volterra integral equations of the second kind with noncompact operators. 相似文献
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Spline Collocation-Interpolation Method for Linear and Nonlinear Cordial Volterra Integral Equations
Gennadi Vainikko 《Numerical Functional Analysis & Optimization》2013,34(1):83-109
We study the convergence and convergence speed of the discontinuous spline collocation and collocation-interpolation methods on uniform grids for linear and nonlinear Volterra integral equations of the second kind with noncompact operators. 相似文献
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Ren-hong Wang You Lu 《计算数学(英文版)》2001,19(3):225-230
1. IntroductionIn recent years, the boundary element methods became a reliable and powerful numerical methods for solving the boundary value problems, such as elastoplasticitys etc. In thesemethods, the original problem is reduced to a boundary integral equation. For the one dimensional boundarys a lot of methods have been put forward recently. But for the two dimensionalboundary situation, it is not so easy to be done because the partition can be very complicated.Since P. Zwart obtained an … 相似文献
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Convergence rate of multiple fractional Stratonovich type integral for Hurst parameter less than 1/2
汪宝彬 《数学物理学报(B辑英文版)》2011,31(5):1694-1708
In this paper, we have investigated the problem of the convergence rate of the multiple integralwhere f ∈ Cn+1([0, T ]n) is a given function, π is a partition of the interval [0, T ] and {BtHi ,π} is a family of interpolation approximation of fractional Brownian motion BtH with Hurst parameter H < 1/2. The limit process is the multiple Stratonovich integral of the function f . In view of known results, the convergence rate is different for different multiplicity n. Under some mild conditions, we obtain that the uniform convergence rate is 2H in the mean square sense, where is the norm of the partition generating the approximations. 相似文献
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The numerical solution of linear Volterra integral equations of the second kind is discussed. The kernel of the integral equation may have weak diagonal and boundary singularities. Using suitable smoothing techniques and polynomial splines on mildly graded or uniform grids, the convergence behavior of the proposed algorithms is studied and a collection of numerical results is given. 相似文献
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Alexei Bespalov Norbert Heuer 《Numerical Methods for Partial Differential Equations》2012,28(5):1466-1480
We apply the hp ‐version of the boundary element method (BEM) for the numerical solution of the electric field integral equation (EFIE) on a Lipschitz polyhedral surface Γ. The underlying meshes are supposed to be quasi‐uniform triangulations of Γ, and the approximations are based on either Raviart‐Thomas or Brezzi‐Douglas‐Marini families of surface elements. Nonsmoothness of Γ leads to singularities in the solution of the EFIE, severely affecting convergence rates of the BEM. However, the singular behavior of the solution can be explicitly specified using a finite set of functions (vertex‐, edge‐, and vertex‐edge singularities), which are the products of power functions and poly‐logarithmic terms. In this article, we use this fact to perform an a priori error analysis of the hp ‐BEM on quasi‐uniform meshes. We prove precise error estimates in terms of the polynomial degree p, the mesh size h, and the singularity exponents. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2012 相似文献
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In this article, we introduce and study the smooth Gauss–Weierstrass singular integral operators on the line of very general kind. We establish their convergence to the unit operator with rates. The estimates are mostly sharp and they are pointwise or uniform. The established inequalities involve the higher order modulus of smoothness. To prove optimality we use mainly the geometric moment theory method. 相似文献