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1.
梅峰太  左莉 《科技通报》2012,28(8):9-11
非线性科学已经被广泛应用于数学、物理、化学、经济等领域。许多非线性现象都可以用非线性偏微分方程来很好地描述,所以得到非线性偏微分方程的解具有重要的意义。在研究非线性科学的同时,出现了一些带有扰动项的非线性偏微分方程。为了研究这种扰动偏微分方程,一些以对称理论为基础的扰动方法相继产生。本文主要研究对称扰动理论在偏微分方程中的应用,寻求偏微分方程的近似对称约化和无穷级数解。  相似文献   

2.
The so-called “percolation operations” which involve simultaneous heat and mass transport are defined in terms of a system of mixed partial differential equations which are nonlinear and include variable coefficients. Second-order interpolation followed by integration over an increment of the time or space variable is proposed as a method for arriving at finite difference equation equivalents of the original partial differential equations. A model change is also used to give physical significance to finite difference equivalents associated with derivatives in the space dimension. It is shown that second-order interpolation has the advantage over linear interpolation that it introduces a factor β which in a stability analysis based on cencentrations offers a range of choices that will insure stable calculation on a digital machine.  相似文献   

3.
获得一类具有连续偏差变元的非线性二阶阻尼泛函微分方程所有解振动的若干充分条件.所得结果包含和推广了已有文献中的相关结论,并给出2个应用实例.  相似文献   

4.
In this paper, we consider the consensus problem of a class of heterogeneous multi-agent systems composed of the linear first-order and second-order integrator agents together with the nonlinear Euler–Lagrange (EL) agents. First, we propose a distributed consensus protocol under the assumption that the parameters of heterogeneous system are exactly known. Sufficient conditions for consensus are presented and the consensus protocol accounting for actuator saturation is developed. Then, by combining adaptive controller and PD controller together, we design a protocol for the heterogeneous system with unknown parameters (in the nonlinear EL dynamics). Based on graph theory, Lyapunov theory and Barbalat's Lemma, the stability of the controllers is proved. Simulation results are also provided to illustrate the effectiveness of the obtained results.  相似文献   

5.
This article investigates the fixed time synchronization (FXTSY) problem of time-varying delayed impulsive inertial neural networks (INNs) with discontinuous activation functions. First, the addressed delayed discontinuous INNs are converted into a first-order differential equation using a generalized variable transformation with suitable tunable variables. Due to the existence of the discontinuities, the delayed discontinuous differential equations are transformed into the differential inclusions by using the differential inclusion theory and set-valued map concepts. Furthermore, by designing the suitable centralized impulsive control and discontinuous control, constructing the novel indefinite type Lyapunov functionals, new algebraic conditions are derived to realize the FXTSY for the leader-following impulsive INNs. Moreover, the settling time is explicitly calculated. Finally, the developed theoretical results are verified by two numerical simulation results.  相似文献   

6.
A method of using orthogonal shifted Legendre polynomials for identifying the parameters of a process whose behaviour can be modelled by a linear differential equation with time-varying coefficients in the form of finite-order polynomials is presented. It is based on the repeated integration of the differential equation and the representations of ∫0ts(τ) dτ = Ps(t) and ts(t) = Rs(t), where P and R are constant matrices and s(t) is a shifted Legendre vector whose elements are shifted Legendre polynomials. The differential input-output equation is converted into a set of overdetermined linear algebraic equations for a least squares solution. The results of simulation studies are included to illustrate the applicability of the method.  相似文献   

7.
Optimal parametrization in numerical construction of curve   总被引：1，自引：0，他引：1  
The application of the optimal parametric continuation method to constructing a solution set curve for a system of nonlinear algebraic or transcendental equations depending on a parameter is considered. There are discussed two approaches to solving this problem—the use of iterative methods and reduction to an initial value problem for a system of ordinary differential equations. The algorithm suggested in this paper can also be used for finding an appropriate initial approximation when solving a system of nonlinear algebraic or transcendental equations not depending on a parameter by an iterative method.  相似文献   

8.
Techniques developed in the Sturm—Liouville problem and its Inverse problem are well known in solving the analysis and synthesis problems of non-uniform distributed networks (or NUDN) (1)-(6), (15). However, very few practical results have been obtained from the theory, especially as regards the synthesis part of the problem. In this paper, we show that the chain matrix of an inhomogeneous ladder network (or IHLN) of N sections has undergone exactly the limit process of first-order difference equation approximation of the corresponding differential equation converges to the chain matrix of the corresponding NUDN uniformly on every compact subset of p = z(s)y(s) plane. Therefore an optimal NUDN is proven to be either symmetrical or antimetrical (7). Specifically, a class of optimal NUDN which is optimal on every subinterval of [O,L] has closed-form solutions, and is proven to be both symmetrical and antimetrical.  相似文献   

9.
In the current work, the Chebyshev collocation method is adopted to find an approximate solution for nonlinear integral equations. Properties of the Chebyshev polynomials and operational matrix are used in the integral equation of a system consisting of nonlinear algebraic equations with the unknown Chebyshev coefficients. Numerical examples are presented to illustrate the method and results are discussed.  相似文献   

10.
This series of papers addresses three interrelated problems: the solution of a variational problem, the solution of integral equations, and the solution of an initial valued system of integrodifferential equations. It will be shown that a large class of variational problems requires the solution of a nonlinear integral equation. It has also been shown that the solution of a nonlinear integral equation is identical to the solution of a Cauchy system. In this paper, we by-pass the nonlinear integral equations and show that the minimization problems directly imply a solution of the Cauchy system. This second paper in the series looks at semi-quadratic functional and scalar functions.  相似文献   

11.
There are few techniques available to numerically solve linear Fredholm integrodifferential-difference equation of high-order. In this paper we show that the Taylor matrix method is a very effective tool in numerically solving such problems. This method transforms the equation and the given conditions into the matrix equations. By merging these results, a new matrix equation which corresponds to a system of linear algebraic equation is obtained. The solution of this system yields the Taylor coefficients of the solution function. Some numerical results are also given to illustrate the efficiency of the method. Moreover, this method is valid for the differential, difference, differential-difference and Fredholm integral equations. In some numerical examples, MAPLE modules are designed for the purpose of testing and using the method.  相似文献   

12.
Recently the optimal filtering problem for nonlinear distributed-parameter systems was treated using various statistical approaches. This paper treats the same problem by using the Fokker-Planck-Kolmogorov equation technique. The arguments used are rather heuristic but the purpose of the paper is mainly to motivate further studies in the area of stochastic differential equations of the distributed-parameter type. An extension is then given to cover the case where the system equations contain unknown stochastic dynamic parameters. The results are illustrated by two practical examples. As a by-product a derivation of the distributed-parameter Fokker-Planck-Kolmogorov equations is given. These equations are useful not only for filtering purposes but also for other probabilistic considerations of distributed-parameter systems.  相似文献   

13.
The space debris removal system (SDRS) of tethered space tug is modelled as a cable dragged flexible spacecraft. The main goal of this paper is to develop a dynamic modeling approach for mode characteristics analysis and forced vibration analysis of the planar motion of a cable dragged flexible spacecraft. Solar arrays of the spacecraft are modelled as multi-beams connected by joints with additional rotating spring where the nonlinear stiffness, damping and friction are considered. Using the Global mode method (GMM), a novel analytical and low-dimensional nonlinear dynamic model is developed for vibration analysis of SDRS to enhance the design capacity for better fulfillment of space tasks. The linear and nonlinear partial differential equations that governing transverse vibration of solar arrays, transverse and longitudinal vibrations of cable are derived, along with the matching and boundary conditions. The natural frequencies and analytical global mode shapes of SDRS are determined, and orthogonality relations of the global mode shapes are established. Dynamical equations of the system are truncated to a set of ordinary differential equations with multiple-DOF. The validity of the method is verified by comparing the natural frequencies obtained from the characteristic equation with those obtained from FEM. Interesting mode localization and mode shift phenomena are observed in mode analysis. Dynamic responses of the system excitated by fluctuation of attitude control torque and short-time attitude control torque are worked out, respectively. Nonlinear behaviors are observed such as hardening, jump and super-harmonic resonances. Residual vibration of the overall system with considering the varous values of nonlinear stiffness, damping coefficient and friction coefficient has shown that the nonlinearity of joints has a great influence on the vibration of the overall system.  相似文献   

14.
In a previous article1 a continuously recording integraph was described, by means of which differential equations, involving only one integration, could be solved. The present article describes a revision of this machine such that an equation involving two successive integrations, corresponding to practically any second-order total differential equation, with all terminal conditions included, can be solved. The need for a workable means of solving the differential equations involving empirical and discontinuous coefficients which occur repeatedly in electrical engineering and physics is recalled. In the machine described such solutions are effected by means of suitable interlinked integrating devices, the result being plotted continuously as a function of the independent variable. Tests and simple solutions show the over-all error to be approximately 1 or 2 per cent. The various sources of this error are discussed.  相似文献   

15.
The effect of non-Darcian flow on the consolidation behavior of clay soils is studied, and its role in the extrapolation of laboratory test results to field problems is evaluated. This is accomplished by postulating a reasonably general four-parameter velocity-gradient relationship which, by proper choice of parameters, is capable of characterizing much of the published experimental data; then, this relationship is combined with the standard assumptions of classical consolidation theory to develop a nonlinear parabolic partial differential equation, which is solved by use of a finite difference technique. The stability and convergence criteria for related linear and quasi-linear equations are empirically extended to the associated nonlinear equations, and a comparison is made between various explicit and implicit finite difference schemes, with the result that a sufficiently accurate and more economical numerical solution is obtained by use of an explicit scheme. Typical solutions for various specific cases confirm and offer an explanation for the well-known phenomenon wherein the time rate of consolidation is found to decrease as the load increment decreases; also, the thickness of the consolidating layer is shown to affect the dimensionless time rate of consolidation. These conditions indicate that laboratory consolidation test results can be applied to a field situation only if appropriate stress and thickness corrections are made.  相似文献   

16.
A procedure is presented whereby the control volume equations for one-dimensional, compressible gas dynamics are cast into first-order, state variable form. These equations are interpreted using causal bond graphs. The resulting bond graph is shown to reduce to the classic I-C chain under acoustic constraints and to a more recently developed model of low speed thermal energy transport subject to associated constraints.Through example it is demonstrated that the control volume bond graph is easily coupled to an overall system model and thus can be digitally simulated as part of the overall nonlinear state space representation. The result is that a very accurate gas dynamic model can be coupled with an overall dynamic system model without requiring a prohibitively large number of equations.  相似文献   

17.
We used two simple control laws based on linear velocity and cubic velocity feedback to suppress the high-amplitude vibrations of a structural dynamic model of the twin-tail assembly of an F-15 fighter when subjected to primary resonance excitations. We developed the nonlinear differential equations of motion and obtained an approximate solution using the method of multiple scales. Then, we conducted bifurcation analyses for the open- and closed-loop responses of the system and investigated theoretically the performance of the control strategies. The theoretical findings indicate that the control laws lead to effective vibration suppression and bifurcation control. Furthermore, we conducted experiments to verify the theoretical analysis. We built a digital control system that consists of a SIMULINK modeling software and a dSPACE controller installed in a personal computer. Actuators made of piezoelectric ceramic material were used. The results show that both laws are effective at suppressing the vibrations. To compare the performance of both techniques, we calculated the power requirements for a simple system.  相似文献   

18.
In this paper, we study stability of a class of stochastic differential delay equations with nonlinear impulsive effects. First, we establish the equivalent relation between the stability of this class of stochastic differential delay equations with impulsive effects and that of a corresponding stochastic differential delay equations without impulses. Then, some sufficient conditions ensuring various stabilities of the stochastic differential delay equations with impulsive effects are obtained. Finally, two examples are also discussed to illustrate the efficiency of the obtained results.  相似文献   

19.
In this paper, the Bagley-Torvik equation, which has an important role in fractional calculus, is solved by generalizing the Taylor collocation method. The proposed method has a new algorithm for solving fractional differential equations. This new method has many advantages over variety of numerical approximations for solving fractional differential equations. To assess the effectiveness and preciseness of the method, results are compared with other numerical approaches. Since the Bagley-Torvik equation represents a general form of the fractional problems, its solution can give many ideas about the solution of similar problems in fractional differential equations.  相似文献   

20.
A new method for the calculation of time responses of lumped time invariant networks is presented. It is based on the numerical inversion of the Laplace transform and involves the computation of the frequency domain function at pre-assigned complex points and forming a weighted sum. The method exactly inverts a certain number of terms of the Taylor expansion of the time response and is thus equivalent to the methods used for the integration of differential equations. This equivalence is established on two examples. The order of integration can be changed between 1 and 46 without any difficulty. Additional properties resulting from the application of the numerical Laplace transform inversion are also discussed and some novel applications indicated.  相似文献   

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