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181.
We consider a second‐order differential operator A( x )=?∑?iaij( x )?j+ ∑?j(bj( x )·)+c( x ) on ?d, on a bounded domain D with Dirichlet boundary conditions on ?D, under mild assumptions on the coefficients of the diffusion tensor aij. The object is to construct monotone numerical schemes to approximate the solution of the problem A( x )u( x )=µ( x ), x ∈D, where µ is a positive Radon measure. We start by briefly mentioning questions of existence and uniqueness introducing function spaces needed to prove convergence results. Then, we define non‐standard stencils on grid‐knots that lead to extended discretization schemes by matrices possessing compartmental structure. We proceed to discretization of elliptic operators, starting with constant diffusion tensor and ending with operators in divergence form. Finally, we discuss W‐convergence in detail, and mention convergence in C and L1 spaces. We conclude by a numerical example illustrating the schemes and convergence results. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
182.
We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam. 相似文献
183.
Certain condition on the second fundamental form of CR submanifolds of maximal CR dimension of complex Euclidean space 总被引:1,自引:0,他引:1
We treat m-dimensional real submanifolds M of complex space forms ̿M when the maximal holomorphic tangent subspace is (m−1)-dimensional. On these manifolds there exists an almost contact structure F which is naturally induced from the ambient space and in this paper we study the condition h(FX,Y)−h(X,FY) = g(FX,Y)η, η∊ T⊥(M), on the structure F and on the second fundamental form h of these submanifolds. Especially when the ambient space ̿M is a complex Euclidean space, we obtain a complete classification of submanifolds M which satisfy these conditions.Mathematics Subject Classifications (2000): 53C15, 53C40, 53B20. 相似文献
184.
A way of determining the flexibility of wood-pulp fibres is developed, which involves i) a precise measurement of the topology
of single-fibres by using a confocal laser scanning microscope and ii) the measurement of the elastic modulus of the fibres
by using a single-fibre fatigue cell. Reported in this paper are the initial results of tests carried out on black spruce
fibres, which have been subjected to three different levels of mechanical refining energy, namely ∼1100, 2300, and 3500 kWh/t.
It is found that the fibre flexibility rises significantly between the first and second energy levels, but it does not change
to the same degree between the second and third ones. The described procedure of measuring the flexibility of fibres may be
used to establish the appropriate refiner energy necessary for the production of a specific grade of paper.
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 115–128, January–February, 2006. 相似文献
185.
1引言对于二阶常微分方程的初值问题y″=g(x,y),y(x_0)=y_0,y′(x_0)=y_0′,x_0(?)x(?)T(1)的数值解法的研究引起人们的广泛兴趣.对于直接积分(1),自从1976年J.D.Lambert和I.A.Waston提出二阶P-稳定方法和1978年G.Dahlquist证明P-稳定常系数线性多步方法的最高相容阶不超过2的重要结论以来,截止目前,已积累了许多高于2阶的P-稳定方法.例如,修正的Numerov方法,混合法(特殊形式RK的方法),多导法,Obrechkoff方法,显式RKN方法,单隐方法和对角隐式RKN方法等(顺便指出,文献[5,16]中所说的高阶方法的相容阶均不超过4).所有这些方法,有些相 相似文献
186.
Yu. V. Zasorin 《Siberian Mathematical Journal》2006,47(4):653-658
We establish a connection between the fundamental solutions to some classes of linear nonstationary partial differential equations and the fundamental solutions to other nonstationary equations with fewer variables. In particular, reduction enables us to obtain exact formulas for the fundamental solutions of some spatial nonstationary equations of mathematical physics (for example, the Kadomtsev-Petviashvili equation, the Kelvin-Voigt equation, etc.) from the available fundamental solutions to one-dimensional stationary equations. 相似文献
187.
Shayne Waldron 《Numerical Algorithms》2006,42(2):171-179
We give an algorithm for computing orthogonal polynomials over triangular domains in Bernstein–Bézier form which uses only the operator of degree raising and its adjoint. This completely avoids the need to choose an orthogonal basis (or tight frame) for the orthogonal polynomials of a given degree, and hence the difficulties inherent in that approach. The results are valid for Jacobi polynomials on a simplex, and show the close relationship between the Bernstein form of Jacobi polynomials, Hahn polynomials and degree raising. 相似文献
188.
Using methods of nonlinear functional analysis, we define the structure of an evolution operator equation of second order that can be formulated in direct variational terms. 相似文献
189.
Yiorgos-Sokratis Smyrlis 《BIT Numerical Mathematics》2006,46(1):163-194
We investigate the Method of Fundamental Solutions (MFS) for the solution of certain elliptic boundary value problems. In
particular, we study the case in which the number of collocation points exceeds the number of singularities, which leads to
an over-determined linear system. In such a case, the resulting linear system is over-determined and the proposed algorithm
chooses the approximate solution for which the error, when restricted to the boundary, minimizes a suitably defined discrete
Sobolev norm. This is equivalent to a weighted least-squares treatment of the resulting over-determined system. We prove convergence
of the method in the case of the Laplace’s equation with Dirichlet boundary data in the disk. We develop an alternative way
of implementing the numerical algorithm, which avoids the inherent ill-conditioning of the MFS matrices. Finally, we present
numerical experiments suggesting that introduction of Sobolev weights improves the approximation.
AMS subject classification (2000) 35E05, 35J25, 65N12, 65N15, 65N35, 65T50 相似文献
190.