求解随机微分方程的二级Milstein方法(英文)

In this paper we discuss two-stage Miistein methods for solving Ito stochastic differential equations （SDEs）. Six fully explicit methods （TSM 1 -- TSM 6） are given in this paper. Their order of strong convergence is proved. The stability properties and numerical results show the effectiveness of these methods in the pathwise approximation of Ito SDEs.     

On the Nonexistence of Laurent Polynomial First Integrals for General Nonlinear Systems

The integrability of a system of ODEs 圣=/(x1is defined as the existence of a sufficiently rich set of first integrals such that its solutions canbe expressed by these integrals.Here,a single-valued function西(。)is called a first integralof the system(1)if it is constant along any solution curve of the system(1).If≯(z)isdifferentiable,then this definition can be written as the condition (筹川瑚=0.The singularity analysis has been proved to be a successful tool for finding integrable systems…     

On the Nonexistence of Laurent Polynomial First Integrals for General Semi－quasihomogeneous Systems

An autonomous system of ODFs which admitting a quasi-homogeneous group of symmetries is called a quasihomogeneous one.     

Existence and Uniqueness of Solutions for a Class of Reaction-diffusion Systems

61.Intr0ducti0nInthispaper,wediscussareactionnetinacombusti0nmodel:V={R,,R2},whereR,andR2aredistinctreacti0nprocesses:Rl:A1+A,-A,,R2:A2+A3-P,A,(j=1,2,3)denotesthereactant,andPdenotestheinertproduct.Thesereactionsareexothermicreactions-LetQ,,Q2standforheatenergiesandU=(U,,U,,U,,U,)forstatevariablesdescribingreactions,whereUoisreactiontemporature,andU,(j=1,2,3)isthemolarityofthej-threactant.AssumethatV,(i=1,2)isthereactantvariablefortheithreactionpr0cess:V,=(Q,,1,-l,l)",V2=(Q,,O,-l,-…     

催化反应中的一类奇摄动边值问题

§1. Introduction We are concered with the singularly perturbed boundary value problemε2y″=y3,(1)y(0)=1, y(1)=2,(2)where ε＞0 is a positive small parameter. This problem arises as models for certain catalytic reactions in chemical engineering. The study of that problem has been paid much attention for the boundary layers of the problem exihibit the behavior of nonexponential decay. There have been some works on this subject ［1］-［4］. In particular, Howes and Chang［1］ gave an accurate…     

A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming

In this paper, on the basis of the logarithmic barrier function and KKT conditions , we propose a combined homotopy infeasible interior-point method (CHIIP) for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.     

用改进的凝聚约束同伦方法求解一类Brouwer不动点问题

In this paper, we provide an aggregate function homotopy interior point method to solve a class of Brouwer fixed-point problems. Compared with the homotopy method (proposed by Yu and Lin, Appl. Math. Comput., 74(1996), 65), the main adavantages of this method are as follows: on the one hand, it can solve the Brouwer fixed-point problems in a broader class of nonconvex subsets Ω in Rn (in this paper, we let Ω = [x ∈ Rn: gi(x) ≤ 0, i = 1,… ,m]); on the other hand, it can also deal with the subsets Ω with larger amount of constraints more effectively.     

非线性系统有理首次积分的不存在性和部分存在性

该文的目的是给出一般非线性系统存在和部分存在有理首次积分的判别准则. 作者给出系统存在有理首次积分的必要条件, 在此基础上进一步给出系统不存在其它有理首次积分(在函数独立的意义下)的判定准则.     

求常微分方程周期解的同伦方法

As an important aspect of applications, it is discussed how to find periodic solutions for ordinary differential equations. By using the homotopy method, a global method for finding those solutions is proposed.