共查询到20条相似文献,搜索用时 62 毫秒
1.
Ron Buckmire 《Numerical Methods for Partial Differential Equations》2004,20(3):327-337
The boundary value problem Δu + λeu = 0 where u = 0 on the boundary is often referred to as “the Bratu problem.” The Bratu problem with cylindrical radial operators, also known as the cylindrical Bratu‐Gelfand problem, is considered here. It is a nonlinear eigenvalue problem with two known bifurcated solutions for λ < λc, no solutions for λ > λc and a unique solution when λ = λc. Numerical solutions to the Bratu‐Gelfand problem at the critical value of λc = 2 are computed using nonstandard finite‐difference schemes known as Mickens finite differences. Comparison of numerical results obtained by solving the Bratu‐Gelfand problem using a Mickens discretization with results obtained using standard finite differences for λ < 2 are given, which illustrate the superiority of the nonstandard scheme. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 327–337, 2004 相似文献
2.
In this paper, we discuss basic properties, a least‐squares problem for row extended matrices and the associated approximation problem. First, we obtain their basic properties by applying their particular structure. Then we derive a general representation of the solutions to the least‐squares problem, and we obtain an expression for the solution to the associated approximation problem. Finally, we provide a perturbation analysis and a perturbation bound for the best approximate solution. The results are illustrated by numerical examples. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
3.
An inverse problem of finding the time‐dependent diffusion coefficient from an integral condition 下载免费PDF全文
Mohammed S. Hussein Daniel Lesnic Mansur I. Ismailov 《Mathematical Methods in the Applied Sciences》2016,39(5):963-980
We consider the inverse problem of determining the time‐dependent diffusivity in one‐dimensional heat equation with periodic boundary conditions and nonlocal over‐specified data. The problem is highly nonlinear and it serves as a mathematical model for the technological process of external guttering applied in cleaning admixtures from silicon chips. First, the well‐posedness conditions for the existence, uniqueness, and continuous dependence upon the data of the classical solution of the problem are established. Then, the problem is discretized using the finite‐difference method and recasts as a nonlinear least‐squares minimization problem with a simple positivity lower bound on the unknown diffusivity. Numerically, this is effectively solved using the lsqnonlin routine from the MATLAB toolbox. In order to investigate the accuracy, stability, and robustness of the numerical method, results for a few test examples are presented and discussed. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
4.
Abdullah Said Erdogan Ali Ugur Sazaklioglu 《Mathematical Methods in the Applied Sciences》2014,37(16):2393-2405
In this paper, a right‐hand side identification problem for a parabolic equation with an overdetermined condition on an observation point is considered. A first and second order of accuracy difference schemes are constructed for obtaining approximate solutions of the problem that arises in two‐phase flow in capillaries. Stability estimates and numerical results are also established. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
5.
Brice Franke 《Mathematische Nachrichten》2007,280(8):851-865
We use rearrangement techniques to investigate the decay of the parabolic Dirichlet problem in a bounded domain. The coefficients of the second order term are used to introduce an isoperimetric problem. The resulting isoperimetric function together with the divergence of the first order coefficients and the value distribution of the zero order part are then used to construct a symmetric comparison equation having a slower heat‐flow than the original equation. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
6.
In this paper we consider an inverse problem for a damped vibration system from the noisy measured eigendata, where the mass, damping, and stiffness matrices are all symmetric positive‐definite matrices with the mass matrix being diagonal and the damping and stiffness matrices being tridiagonal. To take into consideration the noise in the data, the problem is formulated as a convex optimization problem involving quadratic constraints on the unknown mass, damping, and stiffness parameters. Then we propose a smoothing Newton‐type algorithm for the optimization problem, which improves a pre‐existing estimate of a solution to the inverse problem. We show that the proposed method converges both globally and quadratically. Numerical examples are also given to demonstrate the efficiency of our method. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
7.
《Mathematische Nachrichten》2018,291(4):682-698
We find necessary and sufficient conditions for the existence of an ‐solution of the Neumann problem, the Robin problem and the transmission problem for the scalar Oseen equation in three‐dimensional open sets. As a consequence we study solutions of the generalized jump problem. 相似文献
8.
《Mathematical Methods in the Applied Sciences》2018,41(5):1774-1795
This paper is devoted to discuss a multidimensional backward heat conduction problem for time‐fractional diffusion equation with inhomogeneous source. This problem is ill‐posed. We use quasi‐reversibility regularization method to solve this inverse problem. Moreover, the convergence estimates between regularization solution and the exact solution are obtained under the a priori and the a posteriori choice rules. Finally, the numerical examples for one‐dimensional and two‐dimensional cases are presented to show that our method is feasible and effective. 相似文献
9.
The linear‐fractional problem is a generalization of the linear Riemann problem that includes the (non‐linear) factorization problem. In case of normal type it can be equivalently reduced to a family of homogeneous linear vector Riemann problems by space foliation and adequate substitutions. Moreover these are equivalent to systems of non‐homogeneous Toeplitz equations with special data. The reduced problem is solved by matrix factorization in various cases. Procedures for reduction to these cases are exposed. Various modified problems and generalizations are pointed out. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
10.
Jin Cheng Dinghua Xu Masahiro Yamamoto 《Mathematical Methods in the Applied Sciences》1999,22(12):1001-1015
In this paper, we discuss an inverse problem in elasticity for determining a contact domain and stress on this domain. We show that this problem is an ill‐posed problem, and we establish the uniqueness and L2‐conditional stability estimation for the stress. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
11.
Karl Meerbergen Christian Schröder Heinrich Voss 《Numerical Linear Algebra with Applications》2013,20(5):852-868
The critical delays of a delay‐differential equation can be computed by solving a nonlinear two‐parameter eigenvalue problem. The solution of this two‐parameter problem can be translated to solving a quadratic eigenvalue problem of squared dimension. We present a structure preserving QR‐type method for solving such quadratic eigenvalue problem that only computes real‐valued critical delays; that is, complex critical delays, which have no physical meaning, are discarded. For large‐scale problems, we propose new correction equations for a Newton‐type or Jacobi–Davidson style method, which also forces real‐valued critical delays. We present three different equations: one real‐valued equation using a direct linear system solver, one complex valued equation using a direct linear system solver, and one Jacobi–Davidson style correction equation that is suitable for an iterative linear system solver. We show numerical examples for large‐scale problems arising from PDEs. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
12.
The impedance wave diffraction problem by a half‐plane screen is revisited in view of its well‐posedness upon different impedance and wave parameters. The problem is analysed with the help of potential and pseudo‐differential operators. Seven conditions between the impedance and wave numbers are found under which the problem will be well‐posed in Bessel potential spaces. In addition, an improvement of the regularity of the solutions is shown for the previous seven conditions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
13.
In this paper, we consider the Dirichlet and impedance boundary value problems for the Helmholtz equation in a non‐locally perturbed half‐plane. These boundary value problems arise in a study of time‐harmonic acoustic scattering of an incident field by a sound‐soft, infinite rough surface where the total field vanishes (the Dirichlet problem) or by an infinite, impedance rough surface where the total field satisfies a homogeneous impedance condition (the impedance problem). We propose a new boundary integral equation formulation for the Dirichlet problem, utilizing a combined double‐ and single‐layer potential and a Dirichlet half‐plane Green's function. For the impedance problem we propose two boundary integral equation formulations, both using a half‐plane impedance Green's function, the first derived from Green's representation theorem, and the second arising from seeking the solution as a single‐layer potential. We show that all the integral equations proposed are uniquely solvable in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including an incident plane wave, the impedance boundary value problem for the scattered field has a unique solution under certain constraints on the boundary impedance. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
14.
In this paper, we study the forward and the backward in time problems for a class of nonlinear diffusion equations with respect to the pseudo‐differential operator. Herein, we investigate the stability of the solution of the forward problem in relationship with parameters of the pseudo‐differential operator and initial data. Besides, as known, the backward in time problem is instability. Hence, we give a method to regularize the solution of the backward problem in the case of the parameters are perturbed. 相似文献
15.
Frank Bauer Stephan Kannengiesser 《Mathematical Methods in the Applied Sciences》2007,30(12):1437-1451
Magnetic resonance imaging with parallel data acquisition requires algorithms for reconstructing the patient's image from a small number of measured k‐space lines. In contrast to well‐known algorithms like SENSE and GRAPPA and its flavours we consider the problem as a non‐linear inverse problem. Fast computation algorithms for the necessary Fréchet derivative and reconstruction algorithms are given. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
16.
A Riesz–Feller space‐fractional backward diffusion problem with a time‐dependent coefficient: regularization and error estimates 下载免费PDF全文
Nguyen Huy Tuan Dang Duc Trong Dinh Nguyen Duy Hai Duong Dang Xuan Thanh 《Mathematical Methods in the Applied Sciences》2017,40(11):4040-4064
In this paper, we consider a Riesz–Feller space‐fractional backward diffusion problem with a time‐dependent coefficient We show that this problem is ill‐posed; therefore, we propose a convolution regularization method to solve it. New error estimates for the regularized solution are given under a priori and a posteriori parameter choice rules, respectively. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
17.
Duan Huo‐Yuan Liang Guo‐Ping 《Numerical Methods for Partial Differential Equations》2004,20(4):609-623
We consider a finite element discretization of the primal first‐order least‐squares mixed formulation of the second‐order elliptic problem. The unknown variables are displacement and flux, which are approximated by equal‐order elements of the usual continuous element and the normal continuous element, respectively. We show that the error bounds for all variables are optimal. In addition, a field‐based least‐squares finite element method is proposed for the 3D‐magnetostatic problem, where both magnetic field and magnetic flux are taken as two independent variables which are approximated by the tangential continuous and the normal continuous elements, respectively. Coerciveness and optimal error bounds are obtained. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. 相似文献
18.
Michael W. Smiley Changbum Chun 《Numerical Methods for Partial Differential Equations》2000,16(2):194-213
The bifurcation function for an elliptic boundary value problem is a vector field B(ω) on R d whose zeros are in a one‐to‐one correspondence with the solutions of the boundary value problem. Finite element approximations of the boundary value problem are shown to give rise to an approximate bifurcation function Bh(ω), which is also a vector field on R d. Estimates of the difference B(ω) − Bh(ω) are derived, and methods for computing Bh(ω) are discussed. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 194–213, 2000 相似文献
19.
Hoang Luc Nguyen Huy Tuan Nguyen Kirane Mokhtar Xuan Thanh Duong Dang 《Mathematical Methods in the Applied Sciences》2019,42(5):1561-1571
We investigate a backward problem for the Rayleigh‐Stokes problem, which aims to determine the initial status of some physical field such as temperature for slow diffusion from its present measurement data. This problem is well‐known to be ill‐posed because of the rapid decay of the forward process. We construct a regularized solution using the filter regularization method in the Gaussian random noise. Under some a priori assumptions on the exact solution, we establish the expectation between the exact solution and the regularized solution in the L2 and Hm norms. 相似文献
20.
Youcef Amirat Gregory A. Chechkin Rustem R. Gadyl'shin 《Mathematical Methods in the Applied Sciences》2010,33(7):811-830
We study the asymptotic behavior of the eigenelements of the Dirichlet problem for the Laplacian in a two‐dimensional bounded domain with thin shoots, depending on a small parameter ε. Under the assumption that the width of the shoots goes to zero, as ε tends to zero, we construct the limit (homogenized) problem and prove the convergence of the eigenvalues and eigenfunctions to the eigenvalues and eigenfunctions of the limit problem, respectively. Under the additional assumption that the shoots, in a fixed vicinity of the basis, are straight and periodic, and their width and the distance between the neighboring shoots are of order ε, we construct the two‐term asymptotics of the eigenvalues of the problem, as ε→0. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献