求解广义中立型系统的线性多步方法的NGP_G-稳定性

建立了广义中立型延迟系统理论解渐近稳定的充分条件 ,分析了用线性多步方法求解广义中立型延迟系统数值解的稳定性 ,在一定的Lagrange插值条件下 ,证明了数值求解广义中立型系统的线性多步方法NGPG_稳定的充分必要条件是线性多步方法是A_稳定的·     

A semi-lagrangian numerical method for geometric optics type problems

Linear multistep methods (LMMs) are written as irreducible general linear methods (GLMs). A-stable LMMs are shown to be algebraically stable GLMs for strictly positive definite G-matrices. Optimal order error bounds, independent of stiffness, are derived for A-stable methods, without considering one-leg methods (OLMs). As a GLM, the OLM is shown to be the transpose of the LMM. For A-stable methods, the LMM G-matrix is the inverse of the OLM G-matrix. Examples of G-symplectic LMMs are given. AMS subject classification (2000) 65L20     

Thirty years of G-stability

The 1976 paper of G. Dahlquist, [13], has had a wide-ranging impact on our understanding of numerical methods for the solution of stiff differential equation systems. The present paper surveys some of the work of Dahlquist in this area. It also shows how this has led to contributions by other authors. In particular, the paper contains a review of non-linear stability for Runge–Kutta and general linear methods. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65L05, 65L06, 65L20     

Extended graphical representation of polynomials with applications to cybernetics

In this paper,the polynomial of a complex variable s(≡x iy)with realcoefficients K=a_0s~n a_1s~(n-1) …… a_(n-1)s a_n.is graphically represented by three plane curves which are the projections of aspace curve on three coordinate planes of the coordinate system(x,iy.K)inwhich K is confined to be real.The projection on(x,iy)plane is just the rootlocus of the polynomial with K as a real parameter.It is remarkable thatthe equation of the root-locus is m-th degree in y~2,whether n=2m 1 orn=2m 2.In addition to the real curve K.=f(x)in the figure(K,x)thereexists another curve K.which is plotted by the real parts of all complexroots against K.The(K,x)curve is particularly important to determine theabsolute as well as the relative stable interval of K for linear systems.For cybernetics,the(K,iy)curve can be used to show the relation betweenthe nature frequency ω and the gain K.Such three figures are useful forstudying the theory of equation and cybernetics.     

NGP_G-STABILITY OF LINEAR MULTISTEP METHODS FOR SYSTEMS OF GENERALIZED NEUTRAL DELAY DIFFERENTIAL EQUATIONS

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