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861.
This paper is devoted to exact and approximate methods (first of all, direct ones) for the solution of integro-operational equations. Themost attention is paid to the theoretical substantiation of the collocation method for the solution of the mentioned equations within the general theory of approximate methods developed by L. V. Kantorovich. 相似文献
862.
学生空间思维的不足影响了学生对空间曲面的理解和重积分的学习。本文通过二个实例,重点讨论了用MATLAB动态生成空间图形的技巧。 相似文献
864.
In this paper, the local radial point interpolation meshless method (LRPIM) is used for the analysis of two‐dimensional potential flows, based on a local‐weighted residual method with the Heaviside step function as the weighting function over a local subdomain. Trial functions are constructed using radial basis functions. The present method is a truly meshless method based only on a number of randomly located nodes. Integration over the subdomains requires only a simple integration cell to obtain the solution. No element matrix assembly is required and no special treatment is needed to impose the essential boundary conditions. The novelty of the paper is the use of a local Heaviside weight function in the LRPIM, which does not need local domain integration and integrations only on the boundary of the local domains are needed. Effects of the sizes of local subdomain and interpolation domain on the performance of the present method are investigated. The behavior of shape parameters of multiquadrics has been systematically studied. Two numerical tests in groundwater and fluid flows are presented and compared with closed‐form solutions and finite element method. The results show that the use of a local Heaviside weight function in the LRPIM is highly accurate and possesses no numerical difficulties. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
865.
Numerical experiments with several variants of the original weighted essentially non‐oscillatory (WENO) schemes (J. Comput. Phys. 1996; 126 :202–228) including anti‐diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the Euler equations. The TVD Runge–Kutta explicit time‐integrating scheme is adopted for unsteady flow computations and lower–upper symmetric‐Gauss–Seidel (LU‐SGS) implicit method is employed for the computation of steady‐state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which consists of first‐order and high‐order fluxes and allows for a more flexible choice of low‐order schemes. Computations of unsteady oblique shock wave diffraction over a wedge and steady transonic flows over NACA 0012 and RAE 2822 airfoils are presented to test and compare the methods. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady‐state convergence rate are examined. By using the WENO scheme with anti‐diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high‐order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
866.
For stochastic control problems with mixed state-control constraints, we develop a dynamics aggregation method which replaces the stochastic differential or difference equation with a simpler constraint. Solutions of such simplified problems are used to construct a sequence of approximations to the original problem. Convergence properties of the method for both discrete-time and continuous-time models are analyzed in detail. 相似文献
867.
A. A. Borisenko 《Mathematical Notes》2000,67(4):425-432
Locally convex compact hypersurfaces immersed in a hollow simply connected Riemannian space of nonpositive sectional curvature
are considered. They are proved to be convex hypersurfaces homeomorphic to the sphere. A similar result for immersed hypersurfaces
with nonpositive definite second quadratic form of rank no smaller than one is obtained.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 498–507, April, 2000. 相似文献
868.
G. Z. Chelidze 《Mathematical Notes》2000,68(2):263-269
To study intersections of embedded bounded closed sets in Banach space, a numerical parameter was introduced earlier; in a
certain sense, this parameter describes the deviation of the shape of a set from that of a sphere. Critical values of this
parameter for some classes of Banach spaces are determined, a new numerical parameter serving the same purpose is introduced,
and the relation between the two parameters is examined.
Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 303–310, August, 2000. 相似文献
869.
Banach空间中微分方程解的存在与唯一性 总被引:6,自引:0,他引:6
在一般Banach空间中,作者讨论了微分方程的初值问题u=f(t,u),u(0)=x0.在比文[6]中弱Carathodory条件更弱的情况下,不仅放宽了[6]中的一个重要不等式条件,还去掉了另一与之相关的不等式限制,仍获得了初值问题解的存在与唯一性及解的迭代逼近.对周期边值问题也获得了类似结果. 相似文献
870.
We describe a method for representing the nonlinear system of gas dynamics equations in quasilinear form with symmetric coefficient matrices and, moreover, with a positive definite matrix at the time derivative. 相似文献