四阶龙格_库塔法在火控解算中的应用

高炮外弹道微分方程组的实时解算一直是火控领域中一项重点的研究课题。本文介绍了以弹丸质心运动为模型的外弹道微分方程组的龙格库塔解法。同时给出了使用龙格-库塔算法对其进行实时积分解算的流程,并通过MATLAB仿真验证,对从事火控系统设计和论证工作有参考意义。     

A numerical algorithm coupling a bifurcating indicator and a direct method for the computation of Hopf bifurcation points in fluid mechanics

This paper deals with the computation of Hopf bifurcation points in fluid mechanics. This computation is done by coupling a bifurcation indicator proposed recently (Cadou et al., 2006) [1] and a direct method (Jackson, 1987; Jepson, 1981) [2] and [3] which consists in solving an augmented system whose solutions are Hopf bifurcation points. The bifurcation indicator gives initial critical values (Reynolds number, Strouhal frequency) for the direct method iterations. Some classical numerical examples from fluid mechanics, in two dimensions, are studied to demonstrate the efficiency and the reliability of such an algorithm.     

A direct method for the characterization and computation of bifurcation points with corank 2

We will consider an extension of a direct method due to Griewank and Reddien for the characterization and computation of double singular points with corank 2. Singular points which satisfy certain type of symmetry will also be considered. The method used will produce an extended system which does not introduce the null vectors as variables, but gives a good idea bout them. Several numerical examples are presented to demonstrate that the method is efficient.     

数值计算方法课程建设的探索与思考

数值计算方法是一门将数学知识和计算机编程技术相结合的课程,针对工程专业学生学习这门课程存在的困难,阐述了在工程专业开设数值计算方法课程的必要性。结合工程实践教学特点,优化教学模式和方法,提升工程专业学生计算思维能力,使得教学效果更好。     

Chaos induced by the generalized Euler method

In this paper, bifurcation and the chaotic phenomenon in numerical computation are investigated using the generalized Euler method. In this method, the forward and backward Euler methods and the trapezoidal method can be represented as special cases. It will be made clear that, for some computation step size, the solution of the difference equation does not always approximate to the solution of the original differential equation; period-doubling bifurcations and the chaotic phenomenon occur in the solution of the difference equation. Two examples are shown to illustrate the effect of step size.     

A matrix pencil based numerical method for the computation of theGCD of polynomials

The paper presents a new numerical method for the computation of the greatest common divisor (GCD) of an m-set of polynomials of R[s], P _m,d, of maximal degree d. It is based on a previously proposed theoretical procedure (Karcanias, 1989) that characterizes the GCD of P_m,d as the output decoupling zero polynomial of a linear system S(Aˆ,Cˆ) that may be associated with P_m,d . The computation of the GCD is thus reduced to finding the finite zeros of the pencil sW-AW, where W is the unobservable subspace of S(Aˆ,Cˆ). If k=dim W, the GCD is determined as any nonzero entry of the kth compound C_k(sW-AˆW). The method defines the exact degree of GCD, works satisfactorily with any number of polynomials and evaluates successfully approximate solutions     

Fast numerical scheme for gradient vector flow computation using a multigrid method

The gradient vector flow (GVF) deformable model was introduced by Xu and Prince as an effective approach to overcome the limited capture range problem of classical deformable models and their inability to progress into boundary concavities. It has found many important applications in the area of medical image processing. The simple iterative method proposed in the original work on GVF, however, is slow to converge. A new multigrid method is proposed for GVF computation on 2D and 3D images. Experimental results show that the new implementation significantly improves the computational speed by at least an order of magnitude, which facilitates the application of GVF deformable models in processing large medical images     

Regularization and computation of a bifurcation problem with corank 2

This paper deals with a numerical approximation of a bifurcation problem with corank 2. In the neighborhood of the bifurcation point the nonlinear equation is embedded into an extended system. The regular solution of this system including bifurcation point and null space of the corresponding operator derivative allows approximate computation of the bifurcation point and the null space via general discretization and Newton-like methods. In addition, numerical examples are discussed.     

Efficient numerical computation of the plasma dispersion function

An algorithm for the efficient numerical computation of the plasma dispersion function is described, and error criteria and convergence questions are discussed.     

Recursive computation of matrix elements in the numerical renormalization group

The numerical renormalization group is an efficient method to diagonalize model Hamiltonians describing correlated orbitals coupled to conduction states. While only the resulting eigenvalues are needed to calculate the thermodynamical properties for such models, matrix elements of Fermi operators must be evaluated before excitation and transport properties can be computed. The traditional procedure to calculate matrix elements is typically as expensive as the diagonalization of the model Hamiltonian. Here, we present a substantially faster alternative that demands much less memory, yields equally accurate matrix elements and is easier to code.     

Acceleration of the abstract fixpoint computation in numerical program analysis

Static analysis by abstract interpretation aims at automatically proving properties of computer programs, by computing invariants that over-approximate the program behaviors. These invariants are defined as the least fixpoint of a system of semantic equations and are most often computed using the Kleene iteration. This computation may not terminate so specific solutions were proposed to deal with this issue. Most of the proposed methods sacrifice the precision of the solution to guarantee the termination of the computation in a finite number of iterations. In this article, we define a new method which allows to obtain a precise fixpoint in a short time. The main idea is to use numerical methods designed for accelerating the convergence of numerical sequences. These methods were primarily designed to transform a convergent, real valued sequence into another sequence that converges faster to the same limit. In this article, we show how they can be integrated into the Kleene iteration in order to improve the fixpoint computation in the abstract interpretation framework. An interesting feature of our method is that it remains very close to the Kleene iteration and thus can be easily implemented in existing static analyzers. We describe a general framework and its application to two numerical abstract domains: the interval domain and the octagon domain. Experimental results show that the number of iterations and the time needed to compute the fixpoint undergo a significant reduction compared to the Kleene iteration, while its precision is preserved.     

The NumLab numerical laboratory for computation and visualisation

A large range of software environments addresses numerical simulation, interactive visualisation and computational steering. Most such environments are designed to cover a limited application domain, such as finite element or finite difference packages, symbolic or linear algebra computations or image processing. Their software structure rarely provides a simple and extensible mathematical model for the underlying mathematics. Thus, assembling numerical simulations from computational and visualisation blocks, as well as building such blocks is a difficult task for the researcher in numerical simulation.This paper presents the NumLab environment, a single numerical laboratory for computational and visualisation applications. Its software architecture one-to-one models fundamental numerical mathematical concepts and presents a generic framework for a large class of computational applications. Partial and ordinary differential equations, transient boundary value problems, linear and non-linear systems, matrix computations, image and signal processing, and other applications all use the same software architecture and are built in a simple and interactive visual manner. NumLabs one-to-one modelled mathematical concepts are illustrated with various applications.     

On the numerical computation of a structural decomposition in systems and control

In this paper, we develop a new numerical method for a special coordinate basis of a linear time invariant system. Such a special coordinate basis is essentially a structural decomposition which explicitly displays the finite and infinite zero structures, as well as the invertibility structures of the given system. The technique is playing important roles in numerous topics in system and control theory, such as robust control, H/sub /spl infin// and H/sub 2/ optimal control almost disturbance decoupling, and zero placement of linear systems, just to name a few. Our method consists of three steps: reduction by orthogonal transformations, reduction by generalized Sylvester equations, and extraction of infinite zero structure. The performance of our method is illustrated by some numerical examples.     

The order of B-convergence of the Gaussian Runge-Kutta method

In this note the exact order ofB-convergence is determined for them-stage Gaussian Runge-Kutta method. Form=1 this order is 2, whereas form≥2 this order turns out to be onlym.     

A remark on the numerical computation of improper integrals

In this note a transformation is given reducing improper integrals to integrals with smooth integrands. The transformation may be represented in terms of elementary functions and is easily applicable in connection with standard mathematical software for the numerical evaluation of integrals with smooth integrands.     

A Runge-Kutta discontinuous Galerkin method for the Euler equations

This paper presents a Runge-Kutta discontinuous Galerkin (RKDG) method for the Euler equations of gas dynamics from the viewpoint of kinetic theory. Like the traditional gas-kinetic schemes, our proposed RKDG method does not need to use the characteristic decomposition or the Riemann solver in computing the numerical flux at the surface of the finite elements. The integral term containing the non-linear flux can be computed exactly at the microscopic level. A limiting procedure is carefully designed to suppress numerical oscillations. It is demonstrated by the numerical experiments that the proposed RKDG methods give higher resolution in solving problems with smooth solutions. Moreover, shock and contact discontinuities can be well captured by using the proposed methods.     

Numerical computation of electron lenses by the finite element method

The computation of the vector potential distribution in rotationally-symmetric electron lenses can be made with the help og the finite element method. It handles effectively both the complicated geometry of the circuit and the magnetic saturation effects. The paper describes the calculation of the energy functional in one triangle, the mesh-layout method and the numerical methods used to solve the resulting set of linear equations.     

三铰扑翼建模及数值计算

为研究鸟类翅膀展向变形对扑翼气动特性的影响,基于对鸟类翅膀变形的观察,分别用动静法和拉格朗日方程建立三铰扑翼的数学模型,并利用数值计算研究该模型.结果表明：使用NACA0004作为截面的三铰扑翼在对称扑动时能够产生净升力;随着中翼弹性系数比的增大,周期平均升力因数增大,但周期平均阻力因数不存在单调性;三铰扑翼比双铰翼的周期平均升力因数明显小;随着外翼弹性系数比的增大,周期平均升力因数和周期平均阻力因数也不存在单调特性.