共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper is concerned with the nonlinear partial difference equation with continuous variables,where a, σi, τi are positive numbers, hi(x, y, u) ε C(R+ × R+ × R, R), uhi(x, y, u) > 0 for u ≠ 0, hi is nondecreasing in u, i = 1, …, m. Some oscillation criteria of this equation are obtained. 相似文献
2.
Sung Kyu Choi Nam Jip Koo
Binggen Zhang
《Computers & Mathematics with Applications》2001,41(12):1495-1503For the partial difference equations and we shall obtain sufficient conditions for the oscillation of all solutions of these equations. 相似文献
3.
In this paper, we first derive a discrete Gaussian formula and then apply the formula to two classes of nonlinear (parabolic and hyperbolic) partial difference equations with delays to obtain sufficient conditions under which every solution of the two classes of nonlinear partial difference equations with delays is oscillatory. 相似文献
4.
This paper is concerned with the partial difference equation Am+1,n+Am,n+1−Am,n+pm,nAm−k,n−l=0,m,n=0,1,2,…,, where k and l are two positive integers, {pm,n} is a real double sequence. Some new oscillation criteria for this equation are obtained. 相似文献
5.
N. Parhi 《Computers & Mathematics with Applications》2011,62(10):3812-3820
In this paper, sufficient conditions in terms of coefficient functions are obtained for non-oscillation of all solutions of a class of linear homogeneous third order difference equations of the form
6.
We consider linear difference equations with polynomial coefficients over C and their solutions in the form of sequences indexed by the integers (sequential solutions). We investigate the C-linear space of subanalytic solutions, i.e., those sequential solutions that are the restrictions to Z of some analytic solutions of the original equation. It is shown that this space coincides with the space of the restrictions to Z of entire solutions and that the dimension of this space is equal to the order of the original equation.We also consider d-dimensional (d≥1) hypergeometric sequences, i.e., sequential and subanalytic solutions of consistent systems of first-order difference equations for a single unknown function. We show that the dimension of the space of subanalytic solutions is always at most 1, and that this dimension may be equal to 0 for some systems (although the dimension of the space of all sequential solutions is always positive).Subanalytic solutions have applications in computer algebra. We show that some implementations of certain well-known summation algorithms in existing computer algebra systems work correctly when the input sequence is a subanalytic solution of an equation or a system, but can give incorrect results for some sequential solutions. 相似文献
7.
Oscillation of solutions for second-order nonlinear difference equations with nonlinear neutral term 总被引:8,自引:0,他引:8
Zhenguo ZhangJianfeng ChenCaishun Zhang 《Computers & Mathematics with Applications》2001,41(12):1487-1494
Some Riccati type difference inequalities are given for the second-order nonlinear difference equations with nonlinear neutral term. and using these inequalities, we obtain some oscillation criteria for the above equation. 相似文献
8.
We examine the stability properties of a class of LTV difference equations on an infinite-dimensional state space that arise in backstepping designs for parabolic PDEs. The nominal system matrix of the difference equation has a special structure: all of its powers have entries that are −1, 0, or 1, and all of the eigenvalues of the matrix are on the unit circle. The difference equation is driven by initial conditions, additive forcing, and a system matrix perturbation, all of which depend on problem data (for example, viscosity and reactivity in the case of a reaction–diffusion equation), and all of which go to zero as the discretization step in the backstepping design goes to zero. All of these observations, combined with the fact that the equation evolves only in a number of steps equal to the dimension of its state space, combined with the discrete Gronwall inequality, establish that the difference equation has bounded solutions. This, in turn, guarantees the existence of a state-feedback gain kernel in the backstepping control law. With this approach we greatly expand, relative to our previous results, the class of parabolic PDEs to which backstepping is applicable. 相似文献
9.
《国际计算机数学杂志》2012,89(9):1189-1198
The Adomian decomposition method is used to implement the nonhomogeneous multidimensional partial differential equation model problem. The analytic solution of the equation is calculated in the form of a series with easily computable components.The nonhomogeneous problem is quickly solved by observing the self-canceling "noise" terms whose sum vanishes in the limit. Comparing the methodology with some known techniques shows that the present approach is effective and powerful. Two test problems of Mathematical Physics, are discussed to illustrate the effectiveness and the performance of the decomposition method. 相似文献
10.
Ya. E. Romm 《Cybernetics and Systems Analysis》2006,42(1):111-125
For computer analysis of Lyapunov stability, multiplicative criteria are proposed that are based on difference approximations
to solutions of the Cauchy problem. These criteria can be applied to ordinary differential equations in normal form and include
the necessary and sufficient stability conditions. For a system of linear equations with constant coefficients, information
on the characteristic polynomial of the coefficient matrix and its roots is not used. The stability analysis is combined with
difference solution and simulation of error accumulation.
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 127–142, January–February 2006. 相似文献
11.
R.P. Agarwal D. O'Regan Patricia J.Y. Wong 《Computers & Mathematics with Applications》2005,50(10-12):1725-1754
We consider the following system of difference equations, ,where I is a subset of . Our aim is to establish criteria such that the above system has a constantsign periodic and almost periodic solution (u1, u2, …, un). The above problem is also extended to that on , . 相似文献
12.
13.
The second order leapfrog method is used to discretize the linearized KdV equation which is itself a dispersive partial differential equation. The resulting difference equation is solved and analyzed in terms of its dispersion relation and propagation properties. Numerical experiments are included to illustrate some of the results obtained. Finally, a novel aliasing error which affects the propagation of wave packets is presented 相似文献
14.
15.
K. Balla 《Computers & Mathematics with Applications》1998,36(10-12)
Matrix Riccati difference equations are investigated on the infinite index set. Under natural assumptions an existence and uniqueness theorem is proven. The existence of the asymptotic expansion of the solution and computability of its coefficients are shown, provided the coefficients of the equation have such an expansion. 相似文献
16.
《国际计算机数学杂志》2012,89(1):105-117
Past experiments on Hamiltonian circuited simulations of the partial differential equation of the Poisson type have indicated the influences of the Hamiltonian circuits on algebraic structures of coefficients matrices. The need to tend to the usage of finite difference schemes is also observed. A certain Hamiltonian circuit is found to enable the decomposition of the space of simulated points into two subspaces. This paper reports that the space can in fact be separated into four subspaces. Numerical simulations are carried out using a 7-point finite difference star. The results are compared with those obtained when the simulated points are divided into only two disjoint sets. 相似文献
17.
18.
P. Pepe Author Vitae 《Automatica》2005,41(1):107-112
A two-step Liapunov-Krasovskii methodology for checking the asymptotic stability of nonlinear coupled delay differential and continuous time difference equations is proposed here. The feasibility of such methodology is shown by means of Liapunov-Krasovskii functionals with nonconstant kernels in the integrals, for instance discretized Liapunov-Krasovskii ones. An illustrative example taken from the literature, showing the effectiveness of the proposed method, is reported. 相似文献
19.
The input-to-state stability of time-invariant systems described by coupled differential and difference equations with multiple noncommensurate and distributed time delays is investigated in this paper. Such equations include neutral functional differential equations in Hale’s form (which model, for instance, partial element equivalent circuits) and describe lossless propagation phenomena occurring in thermal, hydraulic and electrical engineering. A general methodology for systematically studying the input-to-state stability, by means of Liapunov-Krasovskii functionals, with respect to measurable and locally essentially bounded inputs, is provided. The technical problem concerning the absolute continuity of the functional evaluated at the solution has been studied and solved by introducing the hypothesis that the functional is locally Lipschitz. Computationally checkable LMI conditions are provided for the linear case. It is proved that a linear neutral system in Hale’s form with stable difference operator is input-to-state stable if and only if the trivial solution in the unforced case is asymptotically stable. A nonlinear example taken from the literature, concerning an electrical device, is reported, showing the effectiveness of the proposed methodology. 相似文献
20.
In this note, we prove that linear difference equations in Hilbert space are structurally stable if and only if they have an exponential dichotomy. 相似文献