Rosenbrock schemes with complex coefficients for stiff and differential algebraic systems

Many applied problems are described by differential algebraic systems. Complex Rosenbrock schemes are proposed for the numerical integration of differential algebraic systems by the ?-embedding method. The method is proved to converge quadratically. The scheme is shown to be applicable even to superstiff systems. The method makes it possible to perform computations with a guaranteed accuracy. An equation is derived that describes the leading term of the error in the method as a function of time. An algorithm extending the method to systems of differential equations for complex-valued functions is proposed. Examples of numerical computations are given.     

The Neumann stability of high-order symmetric schemes for convection-diffusion problems

We find a series of sufficient conditions for the Neumann stability of the leapfrog-Euler scheme of arbitrary even order in the spatial coordinates for the three-dimensional convection-diffusion equation.     

Environmental analysis in the Czech Republic: organisation of proficiency testing and its use in laboratory assessment

The history, origin, and development of a system for monitoring and assessing water and other environmental laboratories in the Czech Republic is described. The system started in 1991 and has matured to its present complexity with similarities to the accreditation systems found in other countries. Differences from internationally recognized procedures are being corrected step by step. During the first year of its existence ASLAB, as part of its brief, organised proficiency testing (PT) programs for fifty laboratories. Today the total number of regularly participating laboratories exceeds 700 from the Czech Republic, the Slovak Republic, and Germany. This paper describes the ASLAB PT system, discusses some experiences with its use, and describes the use of PT results in assessment of the competence of laboratories. Received: 12 October 2000 Accepted: 7 January 2001     

An implicit high order finite volume scheme for the solution of 3D Navier–Stokes equations with new discretization of diffusive terms

The computation of three-dimensional viscous flows on complex geometries requiring distorted meshes is of great interest. This paper presents a finite volume solver using a quadratic reconstruction of the unknowns for the advective fluxes computation, and a conservative and consistent discretization of the diffusive terms, based on an extended version of the Coirier's diamond path. A fully implicit time integration procedure is employed with a preconditioned matrix-free GMRES solver.     

Asymptotic relations between the Hahn-type polynomials and Meixner–Pollaczek, Jacobi, Meixner and Krawtchouk polynomials

It has been shown in Ferreira et al. [Asymptotic relations in the Askey scheme for hypergeometric orthogonal polynomials, Adv. in Appl. Math. 31(1) (2003) 61–85], López and Temme [Approximations of orthogonal polynomials in terms of Hermite polynomials, Methods Appl. Anal. 6 (1999) 131–146; The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis, J. Comput. Appl. Math. 133 (2001) 623–633] that the three lower levels of the Askey table of hypergeometric orthogonal polynomials are connected by means of asymptotic relations. In Ferreira et al. [Limit relations between the Hahn polynomials and the Hermite, Laguerre and Charlier polynomials, submitted for publication] we have established new asymptotic connections between the fourth level and the two lower levels. In this paper, we continue with that program and obtain asymptotic expansions between the fourth level and the third level: we derive 16 asymptotic expansions of the Hahn, dual Hahn, continuous Hahn and continuous dual Hahn polynomials in terms of Meixner–Pollaczek, Jacobi, Meixner and Krawtchouk polynomials. From these expansions, we also derive three new limits between those polynomials. Some numerical experiments show the accuracy of the approximations and, in particular, the accuracy in the approximation of the zeros of those polynomials.     

军事行动决策的模糊综合评估

论述了军事行动方案优化决策的评估问题,讨论了评估因素的确定和结构,将定量分析和定性分析的方法结合起来,采用层次分析法确定了因素的相对权重,根据模糊综合评估原理建立从被选方案中选出最佳方案的数学模型.同时结合实例进一步阐明该模型的实施方法步骤.此模型适用性广泛,具有一定的推广应用价值.     

Three‐dimensional incompressible flow calculations using the characteristic based split (CBS) scheme

In this paper, the characteristic based split scheme is employed for the solution of three‐dimensional incompressible viscous flow problems on unstructured meshes. Many algorithm related issues are discussed. Fully explicit and semiimplicit forms of the scheme are explained and employed in the calculation of both isothermal and nonisothermal incompressible flows simulation. The extension of the scheme to porous medium flows is also demonstrated with relevant examples. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulation of free shear flows and far-field sound pressure directivity

An implicit spatial differencing technique with fourth-order accuracy has been developed based on the Pade compact scheme. A dispersion-relation-preserving concept has been incorporated into the numerical scheme. Two-dimensional Euler computation of a spatially developing free shear flow with and without external excitation has been performed to demonstrate the capability of the numerical scheme developed. Results are in good agreement with theory and experimental observation regarding the growth rate of the fluctuating velocity, the convective velocity and the vortex-pairing process. The far-field sound pressure generated by the computed shear flow solution using Lighthill's acoustic analogy shows a strong directivity with a zone of silence at the flow angle.     

Randomized approximation scheme and perfect sampler for closed Jackson networks with multiple servers

In this paper, we propose a fully polynomial-time randomized approximation scheme (FPRAS) for a closed Jackson network. Our algorithm is based on the Markov chain Monte Carlo (MCMC) method. Thus our scheme returns an approximate solution, for which the size of the error satisfies a given bound. To our knowledge, this algorithm is the first polynomial time MCMC algorithm for closed Jackson networks with multiple servers. We propose two new ergodic Markov chains, both of which have a unique stationary distribution that is the product form solution for closed Jackson networks. One of them is for an approximate sampler, and we show that it mixes rapidly. The other is for a perfect sampler based on the monotone coupling from the past (CFTP) algorithm proposed by Propp and Wilson, and we show that it has a monotone update function.     

Roe linearization for the Euler equations augmented by the convective terms from the k–ω turbulence model

This paper describes the method of calculation of the eigenvalues, eigenvectors of the Jacobian matrix of the Euler equations augmented by the convective part of k–ω turbulence model. The equations are 3D and values are expressed in terms of cell normals of a finite volume. The expressions for wave strengths are also found, which are also necessary to calculate the inter‐cell fluxes for Roe's scheme. Copyright © 2007 John Wiley & Sons, Ltd.