共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation, and construct a linear three-level finite difference scheme on a nonuniform grid. The uniform convergence in the sense of discrete L~2 norm is proved and numerical examples are presented. 相似文献
2.
This paper studies the initial boundary value problem of fourth order wave equation with dispersive and dissipative terms. By using multiplier method, it is proven that the global strong solution of the problem decays to zero exponentially as the time approaches infinite, under a very simple and mild assumption regarding the nonlinear term. 相似文献
3.
By finding a parabola solution connecting two equilibrium points of a planar dynamical system,the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown.Some exact explicit parametric representations of kink wave solutions are given.Explicit parameter conditions to guarantee the existence of kink wave solutions are determined. 相似文献
4.
Ref. [1] discussed the existence of positive solutions of quasilinear two-point boundary problems: but it restricts O相似文献
5.
This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form. 相似文献
6.
Chen Shao-jun 《应用数学和力学(英文版)》1993,14(6):545-554
In order to use the second-order 5-point difference scheme mentioned to compute the solution of one dimension unsteady equations
of the direct reflection of the strong plane detonation wave meeting a solid wall barrier, in this paper, we technically construct
the difference schemes of the boundary and sub-boundary of the problem, and deduce the auto-analogue analytic solutions of
the initial value problem, and at the same time, we present a method for the singular property of the initial value problem,
from which we can get a satisfactory computation result of this difficult problem.
The difference scheme used in this paper to deal with the discontinuity problems of the shock wave are valuable and worth
generalization. 相似文献
7.
王德明 《应用数学和力学(英文版)》2008,29(3):361-366
A numerical iterative model was derived from the difference method and a perturbation assumption to calculate the coefficient function of a wave equation. The method was used to solve the disaccord problem of numerical precision between the direct problem model and inverse problem model, and its serial problems using the old method. Numerical simulation calculation shows that the method is feasible and effective. 相似文献
8.
This paper deals with the numerical solution, using finite difference methods, of the hydrodynamic and turbulence energy equations which describe wind wave and tidally induced flow. Calculations are performed using staggered and non-staggered finite difference grids in the vertical, with various time discretizations of the production and dissipation terms in the turbulence energy equations. It is shown that the time discretization of these terms can significantly influence the stability of the solution. The effect of time filtering on the numerical stability of the solution is also considered. The form of the mixing length is shown to significantly influence the bed stress in wind wave problems. A no-slip condition is applied at the sea bed, and the associated high-shear bottom boundary layer is resolved by transforming the equations onto a logarithmic or log-linear co-ordinate system before applying the finite difference scheme. A computationally economic method is developed which remains stable even when a very fine vertical grid (over 200 points) is used with a time step of up to 30 min. 相似文献
9.
李继彬 《应用数学和力学(英文版)》2008,29(11):1391-1398
By using the dynamical system method to study the 2D-generalized Benney- Luke equation, the existence of kink wave solutions and uncountably infinite many smooth periodic wave solutions is shown. Explicit exact parametric representations for solutions of kink wave, periodic wave and unbounded traveling wave are obtained. 相似文献
10.
THE NUMERICAL SOLUTION OF A SINGULARLY PERTURBED PROBLEM FOR SEMILINEAR PARABOLIC DIFFERENTIAL EQUATION 总被引:1,自引:0,他引:1
The numerical solution of a singularly perturbed problem for the semilinear parabolicdifferential equation with parabolic boundary layers is discussed.A nonlinear two-leveldifference scheme is constructed on the special non-uniform grids.The uniform convergenceof this scheme is proved and some numerical examples are given. 相似文献
11.
沈惠川 《应用数学和力学(英文版)》1987,8(1):45-56
This work is the continuation of the discussion of refs. [1–2]. We discuss the dynamics problems of ideal rigid — plastic material in the flow theory of plasticity in this paper. From introduction of the theory of functions of complex variable under Dirac-Pauli representation we can obtain a group of the so-called general equations (i.e. have two scalar equations) expressed by the stream function and the theoretical ratio. In this paper we also testify that the equation of evolution for time in plastodynamics problems is neither dissipative nor disperive, and the eigen-equation in plastodynamics problems is a stationary Schrödinger equation, in which we take partial tensor of stress-increment as eigenfunctions and take theoretical ratio as eigenvalues. Thus, we turn nonlinear plastodynamics problems into the solution of linear stationary Schrödinger equation, and from this we can obtain the general solution of plastodynamics problems with rigid-plastic material. 相似文献
12.
吕咸青 《应用数学和力学(英文版)》1993,14(11):1013-1018
By using the methods of mathematics analysis,we investigate the travelling wave solution of the KdVB equation under the assumption v~2》4μ.We prove that the travelling wave solution is quantitatively similar to the corresponding Burgers shock wave.Then we prove that the absolute error of the general asymptotic expansion is high order quantity of the small parameterε. 相似文献
13.
The elastodynamic problems of piezoelectric hollow cylinders and spheres under radial deformation can be transformed into a second kind Volterra integral equation about a function with respect to time, which greatly simplifies the solving procedure for such elastodynamic problems. Meanwhile, it becomes very important to find a way to solve the second kind Volterra integral equation effectively and quickly. By using an interpolation function to approximate the unknown function, two new recursive formulae were derived, based on which numerical solution can be obtained step by step. The present method can provide accurate numerical results efficiently. It is also very stable for long time calculating. 相似文献
14.
15.
董明德 《应用数学和力学(英文版)》1984,5(2):1151-1162
Despite the great significance of equations with doubly-periodic coefficients in the methods of mathematical physics, the problem of solving Lamé-Helmholtz equation still remains to be tackled. Arscott and Moglich method of double-series expansion as well as Malurkar nonlinear integral equation are incapable of reaching the final explicit solution.Our main result consists in obtaining analytic expressions for ellipsoidal wave functions of four species (i=1,2,3,4) including the well known Lam(α) functions Eci(snα),Ez1(snα) as special cases. This is effected by deriving two Integra-differential equations with variable coefficients and solving them by integral transform. Generalizing Riemann’s idea of P function, we introduce D function to express their transformation properties. 相似文献
16.
Jan ermk 《国际流体数值方法杂志》1998,26(8):977-986
This paper deals with the discretization of the one-dimensional Reynolds equation coupled with the film shape equation, that is used for the numerical solution of elastohydrodynamically lubricated contacts. The derivation of the developed discretization formula is based on the control volume approach. To reduce the discretization error caused by the upwind expression of the Couette (velocity) term, non-symmetric control volumes are used for discretization of the Reynolds equation, while for the elasticity equation the standard approach is used. A numerical method for the solution of the pressure and the film thickness profiles of elastohydrodynamically lubricated isothermal line contacts is presented. Results are presented for chosen typical parameters of a highly loaded contact. To show the formula efficiency, the convergence speed of both the presented discretization formula and a chosen comparative discretization formula (A.A. Lubrecht, Ph.D. Thesis, University of Twente, The Netherlands, 1987 and C.H. Venner, Ph.D. Thesis, University of Twente, The Netherlands, 1991) are checked. The results show that the presented formula gives better approximations of film thickness values for a given number of equidistant grid nodes. Moreover, the presented approach is probably suitable for more sophisticated cases, such as transient situations and elliptical contacts. © 1998 John Wiley & Sons, Ltd. 相似文献
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18.
This paper studies the dynamic behaviors of some exact traveling wave solutions to the generalized Zakharov equation and the
Ginzburg-Landau equation. The effects of the behaviors on the parameters of the systems are also studied by using a dynamical
system method. Six exact explicit parametric representations of the traveling wave solutions to the two equations are given. 相似文献
19.
On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems 总被引:2,自引:0,他引:2
The finite element method is applied to the solution of the transient Fokker-Planck equation for several often cited nonlinear stochastic systems accurately giving, for the first time, the joint probability density function of the response for a given initial distribution. The method accommodates nonlinearity in both stiffness and damping as well as both additive and multiplicative excitation, although only the former is considered herein. In contrast to the usual approach of directly solving the backward Kolmogorov equation, when appropriate boundary conditions are prescribed, the probability density function associated with the first passage problem can be directly obtained. Standard numerical methods are employed, and results are shown to be highly accurate. Several systems are examined, including linear, Duffing, and Van der Pol oscillators. 相似文献
20.
In this paper, we consider a singularly perturbed problem without turning points. On a special diseretization mesh, a coupling difference scheme, resulting from central difference scheme and Abrahamsson-Keller-Kreiss box scheme, is proposed and the second order convergence, uniform in the small parameter, is proved. Finally, numerical resulls are provided. 相似文献