一类A－稳定或L－稳定的经济隐式单块法

一类Ａ－稳定或Ｌ－稳定的经济隐式单块法赵双锁，张国凤（兰州大学数学系）ＡＣＬＡＳＳＯＦＡ－ＳＴＡＢＬＥＯＲＬ－ＳＴＡＢＬＥＥＣＯＮＯＭＩＣＡＬＩＭＰＬＩＣＩＴＳＩＮＧＬＥ－ＢＬＯＣＫＭＥＴＨＯＤＳ￥ＺｈａｏＳｈｕａｎｇ－ｓｕｏ；ＺｈａｎｇＧｕｏ－ｆｅ...     

计算周期解的Lagrange－鞍点算法

计算周期解的Ｌａｇｒａｎｇｅ－鞍点算法张锁春，康羽（中国科学院应用数学研究所）ＬＡＧＲＡＮＧＥ－ＳＡＤＤＬＥＰＯＩＮＴＡＬＧＯＲＩＴＨＭＯＦＣＯＭＰＵＴＡＴＩＮＧＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮ￥ＺｈａｎｇＳｕｏ－ｃｈｕｎ；ＫｕｎｇＹｕ（Ｉｎｓｔｉｔ...     

NEW RESULTS ON THE EXPONENTIAL STABILITY OF NON－STATIONARY POPULATION DYNAMICS

ＮＥＷＲＥＳＵＬＴＳＯＮＴＨＥＥＸＰＯＮＥＮＴＩＡＬＳＴＡＢＩＬＩＴＹＯＦＮＯＮ－ＳＴＡＴＩＯＮＡＲＹＰＯＰＵＬＡＴＩＯＮＤＹＮＡＭＩＣＳ￥（郭宝珠，姚翠珍）ＧｕｏＢａｏｚｈｕ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｂｅｉｊｉ...     

SOLUTIONS CONTAINING DELTA－WAVES OF CAUCHY PROBLEMS FOR A NONSTRICTLY HYPERBOLIC SYSTEM

ＳＯＬＵＴＩＯＮＳＣＯＮＴＡＩＮＩＮＧＤＥＬＴＡ－ＷＡＶＥＳＯＦＣＡＵＣＨＹＰＲＯＢＬＥＭＳＦＯＲＡＮＯＮＳＴＲＩＣＴＬＹＨＹＰＥＲＢＯＬＩＣＳＹＳＴＥＭ￥ＨＵＡＮＧＦＥＩＭＩＮ（黄飞敏）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ,Ｓｈａｎｔｏｕ...     

THE COMPUTATION OF SYMMETRY－BREAKING BIFURCATION POINTS IN Z_2×Z_2－SYMMETRIC NONLINEAR PROBLEMS

ＴＨＥＣＯＭＰＵＴＡＴＩＯＮＯＦＳＹＭＭＥＴＲＹ－ＢＲＥＡＫＩＮＧＢＩＦＵＲＣＡＴＩＯＮＰＯＩＮＴＳＩＮＺ_２×Ｚ_２－ＳＹＭＭＥＴＲＩＣＮＯＮＬＩＮＥＡＲＰＲＯＢＬＥＭＳ￥ＹＥＲＵＩＳＯＮＧＡＮＤＹＡＮＧＺＨＯＮＧＨＵＡＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａ...     

THE LIMIT CYCLES OF THE CUBIC SYSTEMS WITH THREE CF－TYPE SINGULAR POINTS ON A STAIGHT LINE

ＴＨＥＬＩＭＩＴＣＹＣＬＥＳＯＦＴＨＥＣＵＢＩＣＳＹＳＴＥＭＳＷＩＴＨＴＨＲＥＥ　ＣＦ－ＴＹＰＥＳＩＮＧＵＬＡＲＰＯＩＮＴＳＯＮＡＳＴＡＩＧＨＴＬＩＮＥＬｉＸｕｅｐｅｎｇ（李学鹏）（ＦｕｊｉａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎ...     

THE TURNPIKE IN DYNAMIC STOCHASTIC ECONOMIC GROWTH MODELS FOR STATE－CONTINGENT CAPITAL STOCKS

ＴＨＥＴＵＲＮＰＩＫＥＩＮＤＹＮＡＭＩＣＳＴＯＣＨＡＳＴＩＣＥＣＯＮＯＭＩＣＧＲＯＷＴＨＭＯＤＥＬＳＦＯＲＳＴＡＴＥ－ＣＯＮＴＩＮＧＥＮＴＣＡＰＩＴＡＬＳＴＯＣＫＳＣｈｉａｎｇＣｈｉａｏｎｉｎｇ（江胶宁）；ＹｕＸｉａｏｐｅｉ（喻小培）；ＨｅＳｕｉ（何...     

A BRANCH－AND－BOUND ALGORITHM IN THE TOURING－PATH PROBLEM AND ITS COMPUTER IMPLEMENTATION

ＡＢＲＡＮＣＨ－ＡＮＤ－ＢＯＵＮＤＡＬＧＯＲＩＴＨＭＩＮＴＨＥＴＯＵＲＩＮＧ－ＰＡＴＨＰＲＯＢＬＥＭＡＮＤＩＴＳＣＯＭＰＵＴＥＲＩＭＰＬＥＭＥＮＴＡＴＩＯＮＸｕＸｕｓｏｎｇ（徐绪松）（ＳｃｈｏｏｌｏｆＭａｎａｇｅｍｅｎｔ，ＷｕｈａｎＵｎｉｖｅｒｓｉｔ...     

COMPLEMENT AND COMMENTARY OF"ALGEBRAIC CLASSIFICATION OF POLYNOMIAL SYSTEM IN THE PLANE

ＣＯＭＰＬＥＭＥＮＴＡＮＤＣＯＭＭＥＮＴＡＲＹＯＦ＂ＡＬＧＥＢＲＡＩＣＣＬＡＳＳＩＦＩＣＡＴＩＯＮＯＦＰＯＬＹＮＯＭＩＡＬＳＹＳＴＥＭＩＮＴＨＥＰＬＡＮＥ＂杨信安，张剑峰福州大学，邮编：３５０００２ＣＯＭＰＬＥＭＥＮＴＡＮＤＣＯＭＭＥＮＴＡＲＹＯＦ＂...     

SOME TOPOLOGICAL PROPERTIES OF BENZENOID S_n，T_n－ISOMERS WITH n－RADICAL CONNECTION

ＳＯＭＥＴＯＰＯＬＯＧＩＣＡＬＰＲＯＰＥＲＴＩＥＳＯＦＢＥＮＺＥＮＯＩＤＳ_ｎ，Ｔ_ｎ－ＩＳＯＭＥＲＳＷＩＴＨｎ－ＲＡＤＩＣＡＬＣＯＮＮＥＣＴＩＯＮ￥ＺＨＡＮＧＦＵＪＩＡＮＤＣＨＥＮＺＨＩＢＯＡｂｓｔｒａｃｔ：Ｗｅｃｏｎｓｉｄｅｒａｓｅｒｉｅｓｏｆｂｅ...     

一类自适应的单块法及其变步长实现方案

１．引言解 Ｓｔｉｆｆ ＯＤＥｓ初值问题的自开始型单块法已为 ［４, ５］所研究．这里, ｅ＝（１,１,……,１）Ｔ为单位矩阵,当 时见 ［４］,当 ０＜ ａ１＜ ａ２＜…＜ ａｒ＝ ｒ时见［５］。 众所周知,解（１．１）的有效方法通常是隐的．仅当有效地解决了其变步长计算问题并具有有效的迭代法求其解时,这样的方法才能有效地用于实际计算．后者是不言而喻的,前者是由于定步长计算或者往往带来精度的严重损失,或者会带来计算量的严重增加（当存在（ｔ０,Ｔ］的两个子区间,该两区间上的合理积分步长相差悬殊时,就会出现这种…     

On the construction of restricted-denominator exponential W-methods

In this paper we consider the practical construction of exponential W-methods for the solution of large stiff nonlinear initial value problems, based on the restricted-denominator rational approach for the computation of the functions of matrices required. This approach is employed together with the Krylov subspace method based on the Arnoldi algorithm. Two integrators are constructed and tested on some classical stiff equations arising from the semidiscretization of parabolic problems.     

Recent advances in methods for numerical solution of O.D.E. initial value problems

This is a review paper which describes recent advances in numerical methods and computer codes for solving initial value problems of ordinary differential equations. Particular emphasis is placed upon stiff systems.     

On the construction of high order <Emphasis Type="Italic">A</Emphasis>(<Emphasis Type="Italic">α</Emphasis>)-stable hybrid linear multistep methods for stiff IVPs in ODEs

In this paper, we present a class of A(α)-stable hybrid linear multistep methods for numerical solving stiff initial value problems (IVPs) in ordinary differential equations (ODEs). The method considered uses a second derivative like the Enright’s second derivative linear multistep methods for stiff IVPs in ODEs.     

A Class of Multistep Method Containing Second Order Derivatives for Solving Stiff Ordinary Differential Equations

In this paper a general k-step k-order multistep method containing derivatives of second order is given. In particular, a class of k-step (k+1)th-order stiff stable multistep methods for k=3-9 is constructed. Under the same accuracy, these methods are possessed of a larger absolute stability region than those of Gear's [1] and Enright's [2]. Hence they are suitable for solving stiff initial value problems in ordinary differential equations.     

ON THE EXISTENCE AND UNIQUENESS OF SOLUTION OF IMPLICIT HYBRID METHODS

In this paper the existence and uniqueness of the solution of implicit hybrid methods(IHMs)for solving the initial value problems(IVPs)of stiff ordinary differential equations(ODEs)is considered.We provide the coefficient condition and its judging criterion as well as the righthand condition to ensure the existing solution uniquely.     

Convergence of linear multistep and one-leg methods for stiff nonlinear initial value problems

To prove convergence of numerical methods for stiff initial value problems, stability is needed but also estimates for the local errors which are not affected by stiffness. In this paper global error bounds are derived for one-leg and linear multistep methods applied to classes of arbitrarily stiff, nonlinear initial value problems. It will be shown that under suitable stability assumptions the multistep methods are convergent for stiff problems with the same order of convergence as for nonstiff problems, provided that the stepsize variation is sufficiently regular.     

On improving the absolute stability of local extrapolation

Summary A widely used technique for improving the accuracy of solutions of initial value problems in ordinary differential equations is local extrapolation. It is well known, however, that when using methods appropriate for solving stiff systems of ODES, the stability of the method can be seriously degraded if local extrapolation is employed. This is due to the fact that performing local extrapolation on a low order method is equivalent to using a higher order formula and this high order formula may not be suitable for solving stiff systems. In the present paper a general approach is proposed whereby the correction term added on in the process of local extrapolation is in a sense a rational, rather than a polynomial, function. This approach allows high order formulae with bounded growth functions to be developed. As an example we derive anA-stable rational correction algorithm based on the trapezoidal rule. This new algorithm is found to be efficient when low accuracy is requested (say a relative accuracy of about 1%) and its performance is compared with that of the more familiar Richardson extrapolation method on a large set of stiff test problems.     

Mesh selection for stiff two-point boundary value problems

This paper is concerned with the mesh selection algorithm of COLSYS, a well known collocation code for solving systems of boundary value problems. COLSYS was originally designed to solve non-stiff and mildly stiff problems only. In this paper we show that its performance for solving extremely stiff problems can be considerably improved by modifying its error estimation and mesh selection algorithms. Numerical examples indicate the superiority of the modified algorithm.Dedicated to John Butcher on the occasion of his sixtieth birthday     

Trigonometric fitted modification of RADAU5

Implicit Runge-Kutta (RK) methods are in common use when addressing stiff initial value problems (IVP). They usually share the property of A-stability that is of crucial importance in solving the latter type of IVP. Radau IIA family of implicit RK methods is among the preferred ones. Especially its fifth-order representative named RADAU5 has received a lot of attention for use with lax accuracies. Here, we try the lesser possible perturbation of its coefficients. Then, we derive a trigonometric fitted modification that is intended to be applied in periodic IVPs. Numerical tests over a variety of problems with oscillatory solutions justify our effort.