共查询到20条相似文献,搜索用时 15 毫秒
1.
Leszek Klukowski 《Annals of Operations Research》1994,51(5):241-261
In this paper, some probabilistic properties of the nearest adjoining order (NAO) method are presented. They have been obtained under weaker assumptions than those commonly used, i.e. it is not assumed that comparisons are not independent and that probability of comparison errors are known. The results presented comprise the evaluation of the probability of obtaining an errorless solution with the use of the NAO method; asymptotic properties of this solution derived under the assumption that comparisons of different pairs (i.e. pairsx
i
,x
j
andx
r
,x
r
fori r,s andj r,s) are not correlated — for the case of one expert. An extension of results for the case ofN > 1 independent experts is also presented. This extension is accomplished by including an additional step — the aggregation of comparisons made by all experts for each pair of objects. Two ways of such an aggregation are analyzed: the averaging of experts' opinions and the majority principle. In the latter case, the result of the comparison is the same as the opinion of the majority of experts. The results obtained indicate an exponential convergence of the probability of the NAO solution to an errorless one in both cases. However, an application of the majority principle leads to a minimization problem, which is the same as in the case ofN = 1 and is much simpler than that corresponding to averaging of comparisons. 相似文献
2.
In this paper, a finite difference method is used to approximate for the solution of the parabolic partial differential equation of order 2n and error of the method is determined. The resulting system is solved by efficient implicit iterations. In some numerical examples, MAPLE modules are designed for the purpose of testing and using the method. 相似文献
3.
Under some assumptions we find a general solution of the factorization problem for a family of second order difference equations. 相似文献
4.
Yuezhen Ma 《Applied mathematics and computation》2010,215(9):3408-4070
In this paper, we extend the Sun and Zhang’s [24] work on high order finite difference method, which is based on the Richardson extrapolation technique and an operator interpolation scheme for the one and two dimensional steady convection diffusion equations to the three dimensional case. Firstly, we employ a fourth order compact difference scheme to get the fourth order accurate solution on the fine and the coarse grids. Then, we use the Richardson extrapolation technique by combining the two approximate solutions to get a sixth order accurate solution on coarse grid. Finally, we apply an operator interpolation scheme to achieve the sixth order accurate solution on the fine grid. During this process, we use alternating direction implicit (ADI) method to solve the resulting linear systems. Numerical experiments are conducted to verify the accuracy and effectiveness of the present method. 相似文献
5.
Using Nevanlinna theory of the value distribution of meromorphic functions and Wiman-Valiron theory of entire functions, we investigate the problem of growth order of solutions of a type of systems of difference equations, and extend some results of the growth order of solutions of systems of differential equations to systems of difference equations. 相似文献
6.
《Applied Mathematical Modelling》2014,38(15-16):3802-3821
In this paper, our aim is to study the high order finite difference method for the reaction and anomalous-diffusion equation. According to the equivalence of the Riemann–Liouville and Grünwald–Letnikov derivatives under the suitable smooth condition, a second-order difference approximation for the Riemann–Liouville fractional derivative is derived. A fourth-order compact difference approximation for second-order derivative in spatial is used. We analyze the solvability, conditional stability and convergence of the proposed scheme by using the Fourier method. Then we obtain that the convergence order is , where τ is the temporal step length and h is the spatial step length. Finally, numerical experiments are presented to show that the numerical results are in good agreement with the theoretical analysis. 相似文献
7.
New compact finite difference schemes of sixth order are derived for the three dimensional Helmholtz equation, Δu-κ2u=-f. Convergence characteristics and accuracy are compared and a truncation error analysis is presented for a broad range of κ-values. 相似文献
8.
一类高阶非线性中立型差分方程组非振动解的存在性 总被引:1,自引:1,他引:0
贺铁山 《纯粹数学与应用数学》2006,22(2):232-237
研究了一类高阶非线性中立型差分方程组非振动解的存在性.利用Banach空间的压缩映象原理,获得了该方程组存在非振动解的充分条件. 相似文献
9.
Ujjwal Koley Siddhartha Mishra Nils Henrik Risebro Magnus Svärd 《BIT Numerical Mathematics》2009,49(2):375-395
We describe high order accurate and stable finite difference schemes for the initial-boundary value problem associated with
the magnetic induction equations. These equations model the evolution of a magnetic field due to a given velocity field. The
finite difference schemes are based on Summation by Parts (SBP) operators for spatial derivatives and a Simultaneous Approximation
Term (SAT) technique for imposing boundary conditions. We present various numerical experiments that demonstrate both the
stability as well as high order of accuracy of the schemes.
相似文献
10.
Deqiang Liu 《Applied mathematics and computation》2010,215(12):4293-10367
The relationship between {1, 3, 4}-inverses of AB and the product of {1, 3, 4}-inverses of A and B have been studied in this paper. The necessary and sufficient conditions for B{1,3,4}A{1,3,4}⊆(AB){1,3,4}, B{1,3,4}A{1,3,4}⊇(AB){1,3,4} and B{1,3,4}A{1,3,4}=(AB){1,3,4} are given. 相似文献
11.
Frank Uhlig 《Journal of Difference Equations and Applications》2013,19(7):930-941
ABSTRACTZhang Neural Networks rely on convergent 1-step ahead finite difference formulas of which very few are known. Those which are known have been constructed in ad-hoc ways and suffer from low truncation error orders. This paper develops a constructive method to find convergent look-ahead finite difference schemes of higher truncation error orders. The method consists of seeding the free variables of a linear system comprised of Taylor expansion coefficients followed by a minimization algorithm for the maximal magnitude root of the formula's characteristic polynomial. This helps us find new convergent 1-step ahead finite difference formulas of any truncation error order. Once a polynomial has been found with roots inside the complex unit circle and no repeated roots on it, the associated look-ahead ZNN discretization formula is convergent and can be used for solving any discretized ZNN based model. Our method recreates and validates the few known convergent formulas, all of which have truncation error orders at most 4. It also creates new convergent 1-step ahead difference formulas with truncation error orders 5 through 8. 相似文献
12.
13.
《Numerical Methods for Partial Differential Equations》2018,34(6):2237-2266
The Cable equation is one of the most fundamental equations for modeling neuronal dynamics. In this article, we consider a high order compact finite difference numerical solution for the fractional Cable equation, which is a generalization of the classical Cable equation by taking into account the anomalous diffusion in the movement of the ions in neuronal system. The resulting finite difference scheme is unconditionally stable and converges with the convergence order of in maximum norm, 1‐norm and 2‐norm. Furthermore, we present a fast solution technique to accelerate Toeplitz matrix‐vector multiplications arising from finite difference discretization. This fast solution technique is based on a fast Fourier transform and depends on the special structure of coefficient matrices, and it helps to reduce the computational work from required by traditional methods to without using any lossy compression, where and τ is the size of time step, and h is the size of space step. Moreover, we give a compact finite difference scheme and consider its stability analysis for two‐dimensional fractional Cable equation. The applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis. 相似文献
14.
Azmy S. Ackleh Jeremy J. Thibodeaux 《Numerical Methods for Partial Differential Equations》2013,29(6):1821-1836
We present a second‐order finite difference scheme for approximating solutions of a mathematical model of erythropoiesis, which consists of two nonlinear partial differential equations and one nonlinear ordinary differential equation. We show that the scheme achieves second‐order accuracy for smooth solutions. We compare this scheme to a previously developed first‐order method and show that the first order method requires significantly more computational time to provide solutions with similar accuracy. We also compare this numerical scheme with other well‐known second‐order methods and show that it has better capability in approximating discontinuous solutions. Finally, we present an application to recovery after blood loss. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
15.
Yuan Lin Xuejun Gao MingQing Xiao 《Numerical Methods for Partial Differential Equations》2009,25(2):327-346
In this article a sixth‐order approximation method (in both temporal and spatial variables) for solving nonhomogeneous heat equations is proposed. We first develop a sixth‐order finite difference approximation scheme for a two‐point boundary value problem, and then heat equation is approximated by a system of ODEs defined on spatial grid points. The ODE system is discretized to a Sylvester matrix equation via boundary value method. The obtained algebraic system is solved by a modified Bartels‐Stewart method. The proposed approach is unconditionally stable. Numerical results are provided to illustrate the accuracy and efficiency of our approximation method along with comparisons with those generated by the standard second‐order Crank‐Nicolson scheme as well as Sun‐Zhang's recent fourth‐order method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
16.
17.
Sándor Bozóki 《Central European Journal of Operations Research》2008,16(4):345-358
The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method
(LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike
some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex
objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy
method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having
multiple global and local minima.
This research was supported in part by the Hungarian Scientific Research Fund, Grant No. OTKA K 60480. 相似文献
18.
In this paper, we address the impact of uncertainty introduced when the experts complete pairwise comparison matrices, in the context of multi-criteria decision making. We first discuss how uncertainty can be quantified and modeled and then show how the probability of rank reversal scales with the number of experts. We consider the impact of various aspects which may affect the estimation of probability of rank reversal in the context of pairwise comparisons, such as the uncertainty level, alternative preference scales and different weight estimation methods. We also consider the case where the comparisons are carried out in a fuzzy manner. It is shown that in most circumstances, augmenting the size of the expert group beyond 15 produces a small change in the probability of rank reversal. We next address the issue of how this probability can be estimated in practice, from information gathered simply from the comparison matrices of a single expert group. We propose and validate a scheme which yields an estimate for the probability of rank reversal and test the applicability of this scheme under various conditions. The framework discussed in the paper can allow decision makers to correctly choose the number of experts participating in a pairwise comparison and obtain an estimate of the credibility of the outcome. 相似文献
19.
Seakweng Vong Chenyang Shi Pin Lyu 《Numerical Methods for Partial Differential Equations》2019,35(2):493-508
Second order finite difference schemes for fractional advection–diffusion equations are considered in this paper. We note that, when studying these schemes, advection terms with coefficients having the same sign as those of diffusion terms need additional estimates. In this paper, by comparing generating functions of the corresponding discretization matrices, we find that sufficiently strong diffusion can dominate the effects of advection. As a result, convergence and stability of schemes are obtained in this situation. 相似文献
20.
Sufficient conditions for the existence of at least one periodic solution of two classes of nonlinear higher order periodic difference equations are established, respectively. The results show us that sufficient conditions for the existence of T ? periodic solutions of difference equation are different from those ones for the existence of T ? periodic solutions of differential equation. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献