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81.
In this paper, the interpolating moving least-squares (IMLS) method is discussed in details. A simpler expression of the approximation function of the IMLS method is obtained. Compared with the moving least-squares (MLS) approximation, the shape function of the IMLS method satisfies the property of Kronecker δ function. Then the meshless method based on the IMLS method can overcome the difficulties of applying the essential boundary conditions. The error estimates of the approximation function and its first and second order derivatives of the IMLS method are presented in n-dimensional space. The theoretical results show that if the weight function is sufficiently smooth and the order of the polynomial basis functions is big enough, the approximation function and its partial derivatives are convergent to the exact values in terms of the maximum radius of the domains of influence of nodes. Then the interpolating element-free Galerkin (IEFG) method based on the IMLS method is presented for potential problems. The advantage of the IEFG method is that the essential boundary conditions can be applied directly and easily. For the purpose of demonstration, some selected numerical examples are given to prove the theories in this paper. 相似文献
82.
Ping-Fan Dai 《Linear algebra and its applications》2011,434(3):830-840
Doubly B-matrices (DB-matrices), which properly contain B-matrices, are introduced by Peña (2003) [2]. In this paper we present error bounds for the linear complementarity problem when the matrix involved is a DB-matrix and a new bound for linear complementarity problem of a B-matrix. The numerical examples show that the bounds are sharp. 相似文献
83.
Hui Guo 《Applied mathematics and computation》2011,217(9):4682-4690
In this paper, we introduce two novel split least-squares mixed element procedures for pseudo-parabolic equations. By selecting the least-squares functional properly, each procedure can be split into two independent symmetric positive definite sub-procedures. One of sub-procedures is for the primitive unknown variable u, which is the same as the standard Galerkin finite element procedure and the other is for the introduced flux variable σ. Optimal order error estimates are developed. A numerical example is given to show the efficiency of the introduced schemes. 相似文献
84.
85.
An efficient adaptive analysis procedure for node-based smoothed point interpolation method (NS-PIM)
Qian Tang Zhihua ZhongGuiyong Zhang Xu Xu 《Applied mathematics and computation》2011,217(21):8387-8402
This paper presents an efficient adaptive analysis procedure being able to operate in the framework of the node-based smoothed point interpolation method (NS-PIM). The NS-PIM uses three-node triangular cells and is very easy to be implemented, which make it an ideal candidate for adaptive analysis. In the present adaptive procedure, a new error indicator is devised for NS-PIM settings; two ways are proposed to calculate the local critical value; a simple h-type local refinement scheme is adopted and Delaunay technology is used for regenerating optimal new mesh. A number of typical numerical examples involving stress concentration and solution singularities have been tested. The results demonstrate that the present procedure achieves much higher convergence rate results compared to the uniform refinement, and can obtain upper bound solution in strain energy. 相似文献
86.
This article investigates the Galerkin method for an initial boundary value problem for heat convection equations. The new error estimates for the approximate solutions and their derivatives in strong norm are obtained. 相似文献
87.
Consider a radioactive decay chain X1 → ? → Xn→ and let Nn(t) be the amount of Xn at time t. This paper establishes error bounds for large-time approximations to Nn(t) that include and generalize the transient equilibrium approximations and other known approximations. The error bounds allow one to find the range of t for which these approximations can be used with a given degree of precision. 相似文献
88.
Hongchao Kang Shuhuang Xiang 《Applied mathematics and computation》2011,218(7):3553-3564
This paper presents some quadrature methods for a class of highly oscillatory integrals whose integrands may have singularities at the two endpoints of the interval. One is a Filon-type method based on the asymptotic expansion. The other is a Clenshaw-Curtis-Filon-type method which is based on a special Hermite interpolation polynomial and can be evaluated efficiently in O(N log N) operations, where N + 1 is the number of Clenshaw-Curtis points in the interval of integration. In addition, we derive the corresponding error bound in inverse powers of the frequency ω for the Clenshaw-Curtis-Filon-type method for the class of highly oscillatory integrals. The efficiency and the validity of these methods are testified by both the numerical experiments and the theoretical results. 相似文献
89.
Qunying LIAO 《数学年刊B辑(英文版)》2011,32(1):89-98
The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory. The main problem
is to compute the error distance of a received word. Using the Weil bound for character sum estimate, Li and Wan showed that
the error distance can be determined when the degree of the received word as a polynomial is small. In the first part, the
result of Li and Wan is improved. On the other hand, one of the important parameters of an error-correcting code is the dimension.
In most cases, one can only get bounds for the dimension. In the second part, a formula for the dimension of the generalized
trace Reed-Solomon codes in some cases is obtained. 相似文献
90.