共查询到20条相似文献,搜索用时 15 毫秒
1.
We investigate a system of delayed lattice differential system which is a model of pioneer-climax species distributed on one dimensional discrete space. We show that there exists a constant $c^*>0$, such that the model has traveling wave solutions connecting a boundary equilibrium to a co-existence equilibrium for $c\geq c^*$. We also argue that $c^*$ is the minimal wave speed and the delay is harmless. The Schauder's fixed point theorem combining with upper-lower solution technique is used for showing the existence of wave solution. 相似文献
2.
Yuriy Vladimirovich Gandel’ 《Journal of Mathematical Sciences》2010,171(1):74-88
We consider boundary-value problems of mathematical diffraction theory and discuss the possibility of reducing them to boundary
hypersingular integral equations and solving them numerically. The analytic technique of parametric representations of pseudodifferential
and integral operators and the numerical method of discrete singularities are essentially used. We discuss the reasoning in
applying this approach to constructing mathematical models of wave diffraction problems and solving them numerically. 相似文献
3.
Xiu-min Shao Zhi-ling LanInstitute of Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《应用数学学报(英文版)》2002,18(2):295-308
Abstract In this paper, a new kind of discrete non-reflecting boundary conditions is developed.It can be usedfor a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic waveequations and the equations for wave propagation in multi-phase media and so on.In this kind of boundaryconditions,the composition of all artifical reflected waves,but not the individual reflected ones,is consideredand eliminated.Thus, it has a uniform formula for different wave equations.The velocity C_A of the composedreflected wave is determined in the way to make the reflection coefficients minimal,the value of which depends onequations.In this psper,the construction of the boundary conditions illustrated and C_A is found,numericalresults are presented to illustrate the effectiveness of the boundary conditions. 相似文献
4.
We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns. 相似文献
5.
提升钢丝绳动态分析的分段线性化解法 总被引:4,自引:0,他引:4
梁兆正 《应用数学与计算数学学报》1996,(2)
本文在研究提升机绳系动态特性过程中,建立了一类非齐次边界条件混合问题的波动方程;应用离散化方法将非齐次项分段线性化,得到了该类波动方程的半解析解. 相似文献
6.
In this paper, a new domain decomposition method based on the natural boundary reduction, which solves wave problems over an unbounded domain, is suggestted. An circular artificial boundary is introduced. The original unbounded domain is divided into two subdomains, an internal bounded region and external unbounded region outside the artificial boundary. A Dirichlet-Neumann(D-N) alternating iteration algorithm is constructed. We prove that the algorithm is equavilent to preconditional Richardson iteration method. Numerical studies are performed by finite element method. The numerical results show that the convergence rate of the discrete D-N iteration is independent of the finite element mesh size. 相似文献
7.
Jingdong Wei 《Journal of Difference Equations and Applications》2020,26(2):163-170
ABSTRACTIn this paper, we establish the asymptotic boundary of traveling waves (first-component) in a discrete diffusive epidemic model, whose existence is well-known. Meanwhile, we derive the nonexistence of traveling wave solutions with non-positive wave speed. We solve two open problems left in two papers [Fu et al., Nonlinear Convex A. 17 (2016), pp. 1739–1751; Wu, J. Differential Equations 262 (2017), pp. 272–282]. 相似文献
8.
Sorin Micu 《Numerische Mathematik》2002,91(4):723-768
Summary. A numerical scheme for the controlled semi-discrete 1-D wave equation is considered. We analyze the convergence of the boundary
controls of the semi-discrete equations to a control of the continuous wave equation when the mesh size tends to zero. We
prove that, if the high modes of the discrete initial data have been filtered out, there exists a sequence of uniformly bounded
controls and any weak limit of this sequence is a control for the continuous problem. The number of the eliminated frequencies
depends on the mesh size and the regularity of the continuous initial data. The case of the HUM controls is also discussed.
Received March 3, 2001 / Published online October 17, 2001 相似文献
9.
C. Besse M. Ehrhardt I. Lacroix‐Violet 《Numerical Methods for Partial Differential Equations》2016,32(5):1455-1484
We consider the derivation of continuous and fully discrete artificial boundary conditions for the linearized Korteweg–de Vries equation. We show that we can obtain them for any constant velocities and any dispersion. The discrete artificial boundary conditions are provided for two different numerical schemes. In both continuous and discrete case, the boundary conditions are nonlocal with respect to time variable. We propose fast evaluations of discrete convolutions. We present various numerical tests which show the effectiveness of the artificial boundary conditions.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1455–1484, 2016 相似文献
10.
Our numerical method of generating the boundary operator is based on conception of both analytical and discrete transparent boundary conditions. The elastic wave propagation in 2D orthotropic media is considered to show transparency of open circular boundary with proposed NRBC for all tested cases, even where PML approach fails. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
Numerical approximation of the boundary control for the wave equation with mixed finite elements in a square 总被引:1,自引:0,他引:1
12.
Burak Aksoylu Horst Reinhard Beyer Fatih Celiker 《Numerical Functional Analysis & Optimization》2017,38(9):1077-1114
We study nonlocal equations from the area of peridynamics, an instance of nonlocal wave equation, and nonlocal diffusion on bounded domains whose governing equations contain a convolution operator based on integrals. We generalize the notion of convolution to accommodate local boundary conditions. On a bounded domain, the classical operator with local boundary conditions has a purely discrete spectrum, and hence, provides a Hilbert basis. We define an abstract convolution operator using this Hilbert basis, thereby automatically satisfying local boundary conditions. The main goal in this paper is twofold: apply the concept of abstract convolution operator to nonlocal problems and carry out a numerical study of the resulting operators. We study the corresponding initial value problems with prominent boundary conditions such as periodic, antiperiodic, Neumann, and Dirichlet. To connect to the standard convolution, we give an integral representation of the abstract convolution operator. For discretization, we use a weak formulation based on a Galerkin projection and use piecewise polynomials on each element which allows discontinuities of the approximate solution at the element borders. We study convergence order of solutions with respect to polynomial order and observe optimal convergence. We depict the solutions for each boundary condition. 相似文献
13.
We show that the Herglotz wave function with kernel the Tikhonov regularized solution of the far field equation becomes unbounded as the regularization parameter tends to zero iff the wavenumber k belongs to a discrete set of values. When the scatterer is such that the total field vanishes on the boundary, these values correspond to the square root of Dirichlet eigenvalues for ?Δ. When the scatterer is a nonabsorbing inhomogeneous medium these values correspond to so-called transmission eigenvalues. 相似文献
14.
高阶非线性波动方程的有限差分方法 总被引:2,自引:0,他引:2
本文研究一类广泛的高阶非线性波动方程组初边值问题的有限差分格式,用离散泛函分析方法和先验估计的技巧得到了有限差分格式的收敛性。 相似文献
15.
构造并研究了一类具有非局部时滞Schoner竞争反应扩散模型.每一个种群的成熟期是一个常数,而且只有成年种群存在竞争,幼年的种群并不存在竞争,此外种群个体在空间区域中的运动是随机行走的.我们利用Wang,Li和Ruan建立的具有非局部时滞的反应扩散系统的波前解存在性理论,证明了连接两个边界平衡解的行波解的存在性. 相似文献
16.
The approximation sequence for the scattering state is constructed by the solutions for the reduced wave equations in some bounded domains with radiation conditions at their boundary. The corresponding discrete approximation is also considered by the Bubnov-Galerkin method. 相似文献
17.
《Applied Mathematics Letters》2005,18(1):85-90
This paper deals with the chaotic behavior of the solutions of a mixed problem for the one-dimensional wave equation with a quadratic boundary condition. This behavior is studied through the connection between the energy function and quadratic discrete dynamical systems. 相似文献
18.
19.
A. V. Popov 《Journal of Mathematical Sciences》1999,96(4):3415-3418
The boundary conditions ensuring the full absorption of arbitrary paraxial wave packets, described by the parabolic wave equation, are derived in exact form. This provides a mathematically strict method for reducing an infinite domain to a strip or a cylinder when performing numerical calculations.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 239, 1997, pp. 211–217. 相似文献
20.
S. N. Chandler-Wilde 《Mathematical Methods in the Applied Sciences》1997,20(10):813-840
We prove unique existence of solution for the impedance (or third) boundary value problem for the Helmholtz equation in a half-plane with arbitrary L∞ boundary data. This problem is of interest as a model of outdoor sound propagation over inhomogeneous flat terrain and as a model of rough surface scattering. To formulate the problem and prove uniqueness of solution we introduce a novel radiation condition, a generalization of that used in plane wave scattering by one-dimensional diffraction gratings. To prove existence of solution and a limiting absorption principle we first reformulate the problem as an equivalent second kind boundary integral equation to which we apply a form of Fredholm alternative, utilizing recent results on the solvability of integral equations on the real line in [5]. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd. 相似文献