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1.
一类二阶非线性中立型差分方程的振动性   总被引:1,自引:1,他引:0  
研究了二阶非线性中立型差分方程Δ2(xn+pxn-l)+qnf(xn-k)=0的振动性,获得了该类方程振动的三个充分性定理.所得结果将一阶非线性中立型差分方程已有振动性的相应结论推广到了二阶非线性中立型差分方程.  相似文献   

2.
王林峰 《数学研究》2003,36(1):43-50,62
首先研究高阶线性差分方程的整体收敛性,并证明了高阶非线性差分方程各阶导数的整体收敛;进而得到了关于高阶非线性差分方程整体收敛的一个定理,最后利用这个定理部分解决了Ladas提出的一个猜测。  相似文献   

3.
非线性波动方程的交替显-隐差分方法   总被引:4,自引:0,他引:4  
蔚喜军 《计算数学》1998,20(3):225-238
1.引言众所周知,非线性波动方程在自然科学领域有广泛的物理背景,诸如物理、化学反应方程,机械动力学方程,地球物理与大气海洋方程等.差分方法求解非线性波动方程已有研究,如[1]和IZ]就给出了非线性波动方程组的显式和隐式差分格式以及收敛性分析.虽然古典的显式差分格式易于并行计算,但是它的稳定性条件差(条件稳定);古典的隐式差分格式稳定性条件好(绝对稳定);但对非线性问题,一般需要线性化,然后求解一个线性代数方程组,并行计算能力差.本文正是在这样一种前题下,给出了一维问题的一种交替分段显一隐差分格式,…  相似文献   

4.
非线性时滞差分方程的持续生存和渐近性质   总被引:2,自引:0,他引:2  
李万同 《应用数学和力学》2003,24(11):1126-1132
研究了一类非线性时滞差分方程解的渐近性质,得到了方程持续生存和全局吸引的充分条件,这些结果可应用于一类非线性时滞差分方程和时滞离散Logistic模型,并包含了一些已知的结果。  相似文献   

5.
建立了二阶非线性差分方程△(rn△xn-1) Pn△xn-1 qnf(xn)=0的振动准则,所得定理推广和改进了文献中的结果.  相似文献   

6.
二阶非线性差分方程的振动定理   总被引:9,自引:0,他引:9  
本文建立了二阶非线性差分方程新的振动准则.所得定理推广和改进了文献中的结果.并且给出了说明定理应用的例子.  相似文献   

7.
一类非自共轭非线性Schrdinger方程的显式差分格式   总被引:4,自引:1,他引:3  
鲁百年 《计算数学》1989,11(2):118-127
在量子力学与高能物理中,非线性Schrodinger方程很重要,它和KdV方程、BBM方程及Sine-Gordon方程一样,早就引起了人们的注意.郭柏灵讨论了非线性Sch-rodinger方程的适定性与数值方法;吴相辉研究了四点和六点隐差分格式的收敛性和稳定性;常谦顺探讨了守恒差分格式.在[1]中研究了一维晶体和α-螺旋生物分子所产  相似文献   

8.
非线性中立型差分方程的振动性   总被引:15,自引:0,他引:15  
王林 《应用数学》1999,12(1):97-100
本文获得了非线性中立型差分方程Δ(yn-pnyn-k)+qnf(yn-m)=0的所有解振动的几个充分条件。  相似文献   

9.
考虑非线性时滞差分方程x_{n+1}-x_n+p_nf(x_{n-l_1},x_{n-l_2}x_{n-l_m})=0, n=0,1,2, 获得了方程所有解振动的充分条件, 推广并改进了现有文献中的结果.  相似文献   

10.
韩忠月 《数学研究》2007,40(2):173-178
将讨论的差分方程△(rm-1x0-1)+qnxn=anf(xn)看成是其对应的齐次差分方程Δ(rn-1Δyn-1)+qnyn=0的非线性扰动,其中f(x)为[0,∞)连续函数.设对应的齐次差分方程非振动,zn和yn为其主解和非主解.本文将运用压缩映象原理,获得方程存在渐近于其对应齐次方程主解的解的充分条件.并用方程的系数给出其渐近的精确表示.  相似文献   

11.
研究了非线性差分方程xn 1=x^snf(xn,xn-k,…,xn-kr)s∈{1,2,…}得到该系统永久持续生存和全局吸引的充分条件。  相似文献   

12.
Some formulas for well‐defined solutions to four very special cases of a nonlinear fifth‐order difference equation have been presented recently in this journal, where some of them were proved by the method of induction, some are only quoted, and no any theory behind the formulas was given. Here, we show in an elegant constructive way how the general solution to the difference equation can be obtained, from which the special cases very easily follow, which is also demonstrated here. We also give some comments on the local stability results on the special cases of the nonlinear fifth‐order difference equation previously publish in this journal.  相似文献   

13.
The necessary and sufficient condition for an autonomous, ordinary differential equation to be exactly solved by a given Evans-Sanugi, nonlinear, one-step, finite difference method based on ‘classical means’ are derived. A necessary, but not sufficient, condition yields the most general nonlinearity for the differential equation which is independent of the step size. Examples of differential equations for which either nonlinear trapezoidal or nonlinear implicit midpoint methods based on arithmetic, harmonic, contraharmonic, quadratic, geometric, Heronian, centroidal and logarithmic means are exact, are presented. These new exact difference schemes may be useful in future developments of new Denk-Bulirsch, Le-Roux or Kojouhavov-Chen schemes for nonlinear evolution equations with or without blow-up.  相似文献   

14.
In this paper, a 2 nth-order nonlinear difference equation is considered.Using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of periodic solutions.Results obtained complement or improve the existing ones.  相似文献   

15.
非线性时滞差分议程的全局渐近稳定性   总被引:1,自引:0,他引:1  
In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained,xn 1=xn xn-1xn-2 a/xmxm-1 xn-2 a,n=0,1…,where a∈(0,∞) and the initial values x-2,x-1,x0∈(0,∞).As a special case,a conjecture by Ladas is confirmed.  相似文献   

16.
Interest in calculating numerical solutions of a highly nonlinear parabolic partial differential equation with fractional power diffusion and dissipative terms motivated our investigation of a heat equation having a square root nonlinear reaction term. The original equation occurs in the study of plasma behavior in fusion physics. We begin by examining the numerical behavior of the ordinary differential equation obtained by dropping the diffusion term. The results from this simpler case are then used to construct nonstandard finite difference schemes for the partial differential equation. A variety of numerical results are obtained and analyzed, along with a comparison to the numerics of both standard and several nonstandard schemes. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009  相似文献   

17.
High-order compact finite difference method for solving the two-dimensional fourth-order nonlinear hyperbolic equation is considered in this article. In order to design an implicit compact finite difference scheme, the fourth-order equation is written as a system of two second-order equations by introducing the second-order spatial derivative as a new variable. The second-order spatial derivatives are approximated by the compact finite difference operators to obtain a fourth-order convergence. As well as, the second-order time derivative is approximated by the central difference method. Then, existence and uniqueness of numerical solution is given. The stability and convergence of the compact finite difference scheme are proved by the energy method. Numerical results are provided to verify the accuracy and efficiency of this scheme.  相似文献   

18.
In this paper, an initial boundary value problem for nonlinear Klein‐Gordon equation is considered. Giving an additional condition, a time‐dependent coefficient multiplying nonlinear term is determined, and existence and uniqueness theorem for small times is proved. The finite difference method is proposed for solving the inverse problem.  相似文献   

19.
应用不等式估值法讨论了非线性脉冲时滞差分方程解的性质,并得到它的解的一致稳定性的一些充分条件.  相似文献   

20.
本文简要回顾非线性抛物型方程差分方法若干研究工作, 包括周毓麟先生在该研究方向取得的部分研究成果, 并对近年来相关的部分研究进展进行综述, 展望拟开展的研究工作.  相似文献   

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