共查询到20条相似文献,搜索用时 15 毫秒
1.
Collocation Methods for a Class of Volterra Integral Functional Equations with Multiple Proportional Delays
下载免费PDF全文
![点击此处可从《advances in applied mathematics and mechanics.》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Kai Zhang & Jie Li 《advances in applied mathematics and mechanics.》2012,4(5):575-602
In this paper, we apply the collocation methods to a class of
Volterra integral functional equations with multiple proportional
delays (VIFEMPDs). We shall present the existence, uniqueness and
regularity properties of analytic solutions for this type of equations,
and then analyze the convergence orders of the collocation solutions
and give corresponding error estimates. The numerical results verify
our theoretical analysis. 相似文献
2.
While the approximate solutions of one-dimensional nonlinear Volterra-Fredholm integral equations with smooth kermels are now well understood,no systematic studies of the numerical solutions of their multi-dimensional counterparts exist.In this paper,we provide an efficient numerical approach for the multi-dimensional nonlinear Volterra-Fredholm integral equations based on the multi-variate Legendre-collocation approach.Spectral collocation methods for multi-dimensional nonlinear integral equations are known to cause major difficulties from a convergence analysis point of view.Consequently,rigorous error estimates are provided in the weighted Sobolev space showing the exponential decay of the numerical errors.The existence and uniqueness of the numerical solution are established.Numerical experiments are provided to support the theoretical convergence analysis.The results indicate that our spectral collocation method is more flexible with better accuracy than the existing ones. 相似文献
3.
《Nuclear Physics B》1999,549(3):579-612
We investigate the thermodynamic Bethe ansatz (TBA) equations for a system of particles which dynamically interacts via the scattering matrix of affine Toda field theory and whose statistical interaction is of a general Haldane type. Up to the first leading order, we provide general approximated analytical expressions for the solutions of these equations from which we derive general formulae for the ultraviolet scaling functions for theories in which the underlying Lie algebra is simply laced. For several explicit models we compare the quality of the approximated analytical solutions against the numerical solutions. We address the question of existence and uniqueness of the solutions of the TBA equations, derive precise error estimates and determine the rate of convergence for the applied numerical procedure. A general expression for the Fourier transformed kernels of the TBA equations allows one to derive the related Y-systems and a reformulation of the equations into a universal form. 相似文献
4.
5.
In this Letter, we employ finite element method to study a periodic initial value problem for the coupled Schrödinger-KdV equations. For the case of one dimension, this problem is reduced to a system of ordinary differential equations by using a semi-discrete scheme. The conservation properties of this scheme, the existence and uniqueness of the discrete solutions, and error estimates are presented. In numerical experiments, the resulting system of ordinary differential equations are solved by Runge-Kutta method at each time level. The superior accuracy of this scheme is shown by comparing the numerical solutions with the exact solutions. 相似文献
6.
We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations
in material form (“Lagrangian coordinates”). By applying a basic theorem due to Koch, we prove short-time existence and uniqueness
for solutions close to a trivial solution. This trivial, or natural, solution corresponds to a stress-free body in rigid motion. 相似文献
7.
求解对流扩散方程的一种有限分析方法 总被引:2,自引:0,他引:2
本文提出了一种求解线性与拟线性对流扩散方程的有限分析格式,证明了这种格式的解的存在唯一性及绝对稳定性与广义弱稳定性等,大量算例表明它具有较高的精度与很好的稳定性。 相似文献
8.
We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The results point toward the emerging feasibility of direct, exact Maxwell equations modeling of light propagation through many millimeters of biological tissues. More generally, our results have a wider implication: Namely, the study of electromagnetic wave propagation within random media is moving toward exact rather than approximate solutions of Maxwell's equations. 相似文献
9.
We consider the question of the existence of stationary solutions for the Navier Stokes equations describing the flow of a
incompressible fluid past a semi-infinite flat plate at zero incidence angle. By using ideas from the theory of dynamical
systems we analyze the vorticity equation for this problem and show that a symmetry-breaking term fits naturally into the
downstream asymptotic expansion of a solution. Finally, in order to check that our asymptotic expressions can be completed
to a symmetry-breaking solution of the Navier–Stokes equations we solve the problem numerically by using our asymptotic results
to prescribe artificial boundary conditions for a sequence of truncated domains. The results of these numerical computations
a clearly compatible with the existence of such a solution.
Mathematics Subject Classification (2000). 76D05, 76D25, 76M10, 41A60, 35Q35
Supported in part by the Fonds National Suisse. 相似文献
10.
We derive a system of equations which models the motion of linear viscous fluids that undergo isochoric motions in isothermal
processes but not necessarily isochoric ones in non-isothermal processes. The main point is that in contrast to the usual
Oberbeck–Boussinesq approximation we do not neglect dissipative heating. We study Rayleigh–Bénard convection for our system
and investigate existence, uniqueness and regularity of solutions and conditions for the stability of the motionless state.
Received: 26 April 1999 / Accepted: 29 March 2000 相似文献
11.
In this paper we consider a stochastic Ginzburg–Landau equation with impulsive effects. We first prove the existence and uniqueness of the global solution which can be explicitly represented via the solution of a stochastic equation without impulses. Then, based on our obtained result, we study the qualitative properties of the solution, including the boundedness of moments, almost surely exponential convergence and pathwise estimations. Finally, we give a first attempt to study a fractional version of impulsive stochastic Ginzburg–Landau equations. 相似文献
12.
White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical systems in space dimensions d = 1, 2, 3. Whereas existence and uniqueness of weak solutions to these equations are well established in one dimension, the situation is different for d ? 2. Despite their popularity in the applied sciences, higher dimensional versions of these SPDE models are generally assumed to be ill-posed by the mathematics community. We study this discrepancy on the specific example of the two dimensional Allen–Cahn equation driven by additive white noise. Since it is unclear how to define the notion of a weak solution to this equation, we regularize the noise and introduce a family of approximations. Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit. The results strongly suggest that shrinking the mesh size in simulations of the two-dimensional white noise-driven Allen–Cahn equation does not lead to the recovery of a physically meaningful limit. 相似文献
13.
We investigate existence and uniqueness of solutions of a McKean–Vlasov evolution PDE representing the macroscopic behaviour of interacting Fitzhugh–Nagumo neurons. This equation is hypoelliptic, nonlocal and has unbounded coefficients. We prove existence of a solution to the evolution equation and non trivial stationary solutions. Moreover, we demonstrate uniqueness of the stationary solution in the weakly nonlinear regime. Eventually, using a semigroup factorisation method, we show exponential nonlinear stability in the small connectivity regime. 相似文献
14.
We study a solution with an internal transition layer of a one-dimensional boundary value problem for the stationary reaction–advection–diffusion differential equation that arises in mathematical modeling of transport phenomena in the surface layer of the atmosphere in the case of non-uniform vegetation on the assumption of space isotropy along one of the horizontal axes and neutral atmospheric stratification. The parameters of the model at which a boundary value problem has a stable stationary solution with an internal transition layer localized near the boundary between different vegetation types are provided. The existence of such a solution and its local Lyapunov stability and uniqueness are proven. The results can be used for developing multidimensional substance transfer models in the case of a spatial heterogeneity. 相似文献
15.
We study the existence and the uniqueness of stationary solutions for discrete velocity models of the Boltzmann equation in
the first half space. We obtain a sufficient condition that guarantees the existence and the uniqueness of solutions connecting
the given boundary data and the Maxwellian state at a spatially asymptotic point. First, a sufficient condition is obtained
for the linearized system. Then this result as well as the contraction mapping principle is applied to prove the existence
theorem for the nonlinear equation. Also, we show that the stationary wave approaches the Maxwellian state exponentially at
a spatially asymptotic point.
We also discuss some concrete models of Boltzmann type as an application of our general theory. Here, it turns out that our
sufficient condition is general enough to cover many concrete models.
Received: 7 December 1998 / Accepted: 27 April 1999 相似文献
16.
Demetrios Christodoulou 《Communications in Mathematical Physics》1986,105(3):337-361
In this paper we begin the study of the global initial value problem for Einstein's equations in the spherically symmetric case with a massless scalar field as the material model. We reduce the problem to a single nonlinear evolution equation. Taking as initial hypersurface a future light cone with vertex at the center of symmetry, we prove, the local, in retarded time, existence and global uniqueness of classical solutions. We also prove that if the initial data is sufficiently small there exists a global classical solution which disperses in the infinite future.Research supported in part by National Science Foundation grants MCS-8201599 to the Courant Institute and PHY-8318350 to Syracuse University 相似文献
17.
We study the singularity formation of smooth solutions of the relativistic Euler equations in (3 + 1)-dimensional spacetime
for both finite initial energy and infinite initial energy. For the finite initial energy case, we prove that any smooth solution,
with compactly supported non-trivial initial data, blows up in finite time. For the case of infinite initial energy, we first
prove the existence, uniqueness and stability of a smooth solution if the initial data is in the subluminal region away from
the vacuum. By further assuming the initial data is a smooth compactly supported perturbation around a non-vacuum constant
background, we prove the property of finite propagation speed of such a perturbation. The smooth solution is shown to blow
up in finite time provided that the radial component of the initial ``generalized' momentum is sufficiently large. 相似文献
18.
In this paper, we consider the global well-posedness and long-time dynamics for the three-dimensional viscous primitive equations
describing the large-scale oceanic motion under a random forcing, which is an additive white in time noise. We firstly prove
the existence and uniqueness of global strong solutions to the initial boundary value problem for the stochastic primitive
equations. Subsequently, by studying the asymptotic behavior of strong solutions, we obtain the existence of random attractors
for the corresponding random dynamical system. 相似文献
19.
We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method. 相似文献
20.
Jos Luis Díaz Palencia Saeed ur Rahman Antonio Naranjo Redondo 《Entropy (Basel, Switzerland)》2022,24(7)
The goal of this study is to provide an analysis of a Fisher-KPP non-linear reaction problem with a higher-order diffusion and a non-linear advection. We study the existence and uniqueness of solutions together with asymptotic solutions and positivity conditions. We show the existence of instabilities based on a shooting method approach. Afterwards, we study the existence and uniqueness of solutions as an abstract evolution of a bounded continuous single parametric (t) semigroup. Asymptotic solutions based on a Hamilton–Jacobi equation are then analyzed. Finally, the conditions required to ensure a comparison principle are explored supported by the existence of a positive maximal kernel. 相似文献