共查询到20条相似文献,搜索用时 15 毫秒
1.
Xiang-Tuan Xiong 《Journal of Computational and Applied Mathematics》2010,233(8):1723-1732
We investigate a Cauchy problem for the Helmholtz equation. A modified boundary method is used for solving this ill-posed problem. Some Hölder-type error estimates are obtained. The numerical experiment shows that the modified boundary method works well. 相似文献
2.
In this paper, we study a fractional Tikhonov regularization method (FTRM) for solving a Cauchy problem of Helmholtz equation in the frequency domain. On the one hand, the FTRM retains the advantage of classical Tikhonov method. On the other hand, our method can prevent the effect of oversmoothing of classical Tikhonov method and conveniently control the amount of damping. The convergence error estimates between the exact solution and its regularization approximation are constructed. Several interesting numerical examples are provided, which validate the effectiveness of the proposed method. 相似文献
3.
Ai-Lin Qian Xiang-Tuan Xiong 《Journal of Computational and Applied Mathematics》2010,233(8):1969-1979
In this paper, we consider the Cauchy problem for the Helmholtz equation in a rectangle, where the Cauchy data is given for y=0 and boundary data are for x=0 and x=π. The solution is sought in the interval 0<y≤1. A quasi-reversibility method is applied to formulate regularized solutions which are stably convergent to the exact one with explicit error estimates. 相似文献
4.
In this paper, the Cauchy problem for the Helmholtz equation is investigated. It is known that such problem is severely ill-posed. We propose a modified regularization method to solve it based on the solution given by the method of separation of variables. Convergence estimates are presented under two different a-priori bounded assumptions for the exact solution. Finally, numerical examples are given to show the effectiveness of the proposed numerical method. 相似文献
5.
The paper is concerned with the problem of reconstruction of acoustic or electromagnetic field from inexact data given on an open part of the boundary of a given domain. A regularization concept is presented for the moment problem that is equivalent to a Cauchy problem for the Helmholtz equation. A method of regularization by projection with application of the Meyer wavelet subspaces is introduced and analyzed. The derived formula, describing the projection level in terms of the error bound of the inexact Cauchy data, allows us to prove the convergence and stability of the method. 相似文献
6.
In this paper, we consider a Cauchy problem for the Helmholtz equation in a rectangle. An optimal filtering method is presented for approximating the solution of this problem, and the Hölder type error estimate is obtained. Numerical illustration shows that the method works effectively. 相似文献
7.
In this paper, the Cauchy problem for the Helmholtz equation is investigated. By Green’s formulation, the problem can be transformed into a moment problem. Then we propose a modified Tikhonov regularization algorithm for obtaining an approximate solution to the Neumann data on the unspecified boundary. Error estimation and convergence analysis have been given. Finally, we present numerical results for several examples and show the effectiveness of the proposed method. 相似文献
8.
In this paper, we investigate a Cauchy problem associated with Helmholtz-type equation in an infinite “strip”. This problem is well known to be severely ill-posed. The optimal error bound for the problem with only nonhomogeneous Neumann data is deduced, which is independent of the selected regularization methods. A framework of a modified Tikhonov regularization in conjunction with the Morozov’s discrepancy principle is proposed, it may be useful to the other linear ill-posed problems and helpful for the other regularization methods. Some sharp error estimates between the exact solutions and their regularization approximation are given. Numerical tests are also provided to show that the modified Tikhonov method works well. 相似文献
9.
We consider a Cauchy problem for the modified Helmholtz equation. A conditional stability estimate is proved. Two order optimal regularization methods and error estimates are investigated. Numerical experiment shows that these methods work well. 相似文献
10.
G.H. Zheng 《Journal of Computational and Applied Mathematics》2010,233(10):2631-4094
In this paper, a Cauchy problem for the time fractional advection-dispersion equation (TFADE) is investigated. Such a problem is obtained from the classical advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order . We show that the Cauchy problem of TFADE is severely ill-posed and further apply a spectral regularization method to solve it based on the solution given by the Fourier method. The convergence estimate is obtained under a priori bound assumptions for the exact solution. Numerical examples are given to show the effectiveness of the proposed numerical method. 相似文献
11.
This paper is concerned with the Cauchy problem connected with the Helmholtz equation. On the basis of the denseness of Herglotz wavefunctions, we propose a numerical method for obtaining an approximate solution to the problem. We analyze the convergence and stability with a suitable choice of regularization method. Numerical experiments are also presented to show the effectiveness of our method. 相似文献
12.
V. Zh. Sakbaeva 《Proceedings of the Steklov Institute of Mathematics》2008,261(1):253-261
We study the Cauchy problem for an equation whose generating operator is degenerate on some subset of the coordinate space. To approximate a solution of the degenerate problem by solutions of well-posed problems, we define a class of regularizations of the degenerate operator in terms of conditions on the spectral properties of approximating operators. We show that the behavior (convergence, compactness, and the set of partial limits in some topology) of the sequence of solutions of regularized problems is determined by the deficiency indices of the degenerate operator. We define an approximative solution of the degenerate problem as the limit of the sequence of solutions of regularized problems and analyze the dependence of the approximative solution on the choice of an admissible regularization. 相似文献
13.
Jim Douglas Juan E. Santos Dongwoo Sheen 《Numerical Methods for Partial Differential Equations》2001,17(5):475-494
Nonconforming Galerkin methods for a Helmholtz‐like problem arising in seismology are discussed both for standard simplicial linear elements and for several new rectangular elements related to bilinear or trilinear elements. Optimal order error estimates in a broken energy norm are derived for all elements and in L2 for some of the elements when proper quadrature rules are applied to the absorbing boundary condition. Domain decomposition iterative procedures are introduced for the nonconforming methods, and their convergence at a predictable rate is established. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 475–494, 2001 相似文献
14.
An iterative method for a Cauchy problem for the heat equation 总被引:1,自引:0,他引:1
** Email: tomjo{at}itn.liu.se An iterative method for reconstruction of the solution to aparabolic initial boundary value problem of second order fromCauchy data is presented. The data are given on a part of theboundary. At each iteration step, a series of well-posed mixedboundary value problems are solved for the parabolic operatorand its adjoint. The convergence proof of this method in a weightedL2-space is included. 相似文献
15.
16.
章志飞 《高校应用数学学报(A辑)》2003,18(2):179-183
利用半群S(t)=e^—t(—∠←)θ/2=F^—1e—t^|ε|^0F的L^p-L^r估计,证明了修正Navier—Stokes方程解的存在性和惟一性。 相似文献
17.
In this study we establish global well-posedness of the Cauchy problem for a higher-order Boussinesq equation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
Sh. Yarmukhamedov 《Mathematical Notes》1975,18(1):615-618
We obtain a formula which expresses the values of a harmonic function at points of a threedimensional domain in terms of its values and the values of its normal derivative on a portion of the domain boundary. 相似文献
19.
A. V. Faminskii 《Journal of Mathematical Sciences》1990,50(1):1381-1420
Nonlocal results on the existence, uniqueness, continuous dependence on the initial data, and intrinsic regularity of generalized solutions of the Cauchy problem for the Korteweg-de Vries equation and its generalizations are established.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 13, pp. 56–105, 1988. 相似文献
20.
Numerical Algorithms - We investigate the Cauchy problem associated with the Helmholtz equation in three dimensions, namely the numerical reconstruction of the primary field (Dirichlet data) and... 相似文献