共查询到20条相似文献,搜索用时 0 毫秒
1.
This paper investigates the inverse problem of determining a heat source in a parabolic equation where data are given at some fixed location. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. A central difference regularization method is given and an order optimal stability estimate is obtained. Numerical results for several benchmark test problems indicate that the central difference regularization method is an accurate and flexible method to determine the unknown time-dependent heat source. 相似文献
2.
This paper is to discuss the inverse problem of determining a spacewise dependent heat source in one-dimensional heat equation in a bounded domain where data is given at some fixed time. This problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. The regularization solution is given by a simplified Tikhonov regularization. For this regularization solution, the Hölder type stability estimate between the regularization solution and the exact solution is obtained. Numerical examples show that the regularization method is effective and stable. 相似文献
3.
Xue-ping Luo 《Optimization Letters》2014,8(3):877-887
The purpose of this paper is to study Tikhonov regularization methods for inverse variational inequalities. A rather weak coercivity condition is given which guarantees that the solution set of regularized inverse variational inequality is nonempty and bounded. Moreover, the perturbation analysis for the solution set of regularized inverse variational inequality is established. As an application, we show that solutions of regularized inverse variational inequalities form a minimizing sequence of the D-gap function under a mild condition. 相似文献
4.
Chu-Li Fu You-Bin Zhu Chun-Yu Qiu 《Journal of Mathematical Analysis and Applications》2003,288(1):212-222
In this paper we consider an inverse heat conduction problem which appears in some applied subjects. This problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. The Meyer wavelets are applied to formulate a regularized solution which is convergent to exact one on an acceptable interval when data error tends to zero. 相似文献
5.
This paper is devoted to discuss an inverse problem of determining an unknown source on the Poisson equation. This is a mildly ill-posed problem. Two regularization methods, one based on the mollification of the data and the other based on the modification of the ‘kernel’ of the solution, are proposed to solve this problem. The convergence estimates between the exact solution and the regularization solution are presented using a priori regularization parameter choice rule. Numerical results are presented to illustrate the accuracy and efficiency of the proposed methods. 相似文献
6.
The revised generalized Tikhonov method for the backward time-fractional diffusion equation
下载免费PDF全文
![点击此处可从《Journal of Applied Analysis & Computation》网站下载免费的PDF全文](/ch/ext_images/free.gif)
Arumugam Deiveegan Juan J. Nieto Periasamy Prakash 《Journal of Applied Analysis & Computation》2019,9(1):45-56
In this paper, we solve the backward problem for a time-fractional diffusion equation with variable coefficients in a bounded domain by using the revised generalized Tikhonov regularization method. Convergence estimates under an a-priori and a-posteriori regularization parameter choice rules are given. Numerical example shows that the proposed method is effective and stable. 相似文献
7.
In this paper we propose a numerical reconstruction method for solving a backward heat conduction problem. Based on the idea
of reproducing kernel approximation, we reconstruct the unknown initial heat distribution from a finite set of scattered measurement
of transient temperature at a fixed final time. Standard Tikhonov regularization technique using the norm of reproducing kernel
is adopt to provide a stable solution when the measurement data contain noises. Numerical results indicate that the proposed
method is stable, efficient, and accurate. 相似文献
8.
A. M. Denisov E. V. Zakharov A. V. Kalinin V. V. Kalinin 《Moscow University Computational Mathematics and Cybernetics》2008,32(2):61-68
The inverse electrocardiography problem related to medical diagnostics is considered in terms of potentials. Within the framework of the quasi-stationary model of the electric field of the heart, the solution of the problem is reduced to the solution of the Cauchy problem for the Laplace equation in R 3. A numerical algorithm based on the Tikhonov regularization method is proposed for the solution of this problem. The Cauchy problem for the Laplace equation is reduced to an operator equation of the first kind, which is solved via minimization of the Tikhonov functional with the regularization parameter chosen according to the discrepancy principle. In addition, an algorithm based on numerical solution of the corresponding Euler equation is proposed for minimization of the Tikhonov functional. The Euler equation is solved using an iteration method that involves solution of mixed boundary value problems for the Laplace equation. An individual mixed problem is solved by means of the method of boundary integral equations of the potential theory. In the study, the inverse electrocardiography problem is solved in region Ω close to the real geometry of the torso and heart. 相似文献
9.
In this paper, we consider an inverse problem of determining an unknown source for the Poisson equation. Since this problem is mildly ill-posed, we apply a central difference regularization method to solve this problem. Furthermore, the convergence estimate is established under a priori choice of the regularization parameter. Some numerical results verify that the proposed method is stable and effective. 相似文献
10.
逆热传导问题是数学物理反问题中的热点和前沿课题之一,在钢铁生产等领域中具有重要的应用背景.讨论一个多层介质中的逆热传导问题,它是一个极度不适定问题.通过傅里叶截断方法构造正则化近似解,并给出相应的稳定性估计. 相似文献
11.
In this paper, we consider a spherically symmetric inverse heat conduction problem of determining the internal surface temperature of a hollow sphere from the measured data at a fixed location inside it. This is an ill-posed problem in the sense that the solution (if it exists) does not depend continuously on the data. A Tikhonov type’s regularization method and a Fourier regularization method are applied to formulate regularized solutions which are stably convergent to the exact ones with order optimal error estimates. 相似文献
12.
《Applied Mathematical Modelling》2005,29(11):1022-1039
The conjugate gradient method (CGM) with adjoint equations was applied to a generalized inverse force vibration problem to simultaneously estimate the unknown time-dependent external forces in a multiple-degree-of-freedom damped system with time-dependent system parameters by using the simulated measured system displacement. The accuracy of the inverse analysis for a two-degree-of-freedom problem is examined by using the simulated exact and inexact displacement measurements in the numerical experiments. Results have shown that the excellent estimations on the external forces can be obtained with any arbitrary initial guesses within a very short CPU time on a Pentium III-500 MHz PC. 相似文献
13.
Nguyen Buong 《Computational Mathematics and Mathematical Physics》2007,47(10):1583-1588
The goal of this study is to analyze the Tikhonov regularization method as applied to a general nonlinear optimization problem
that has been previously reduced to an unconstrained optimization problem. The stability properties of the method are examined,
and its convergence is proved.
The text was submitted by the author in English. 相似文献
14.
This paper is devoted to solve a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain by the Tikhonov regularization method. Based on the eigenfunction expansion of the solution, the backward problem for searching the initial data is changed to solve a Fredholm integral equation of the first kind. The conditional stability for the backward problem is obtained. We use the Tikhonov regularization method to deal with the integral equation and obtain the series expression of solution. Furthermore, the convergence rates for the Tikhonov regularized solution can be proved by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule. Two numerical examples in one-dimensional and two-dimensional cases respectively are investigated. Numerical results show that the proposed method is effective and stable. 相似文献
15.
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
16.
Jingjun Zhao Songshu Liu Tao Liu 《Mathematical Methods in the Applied Sciences》2013,36(11):1399-1408
In this paper, we investigate a problem of the identification of an unknown source on Poisson equation from some fixed location. A conditional stability estimate for an inverse heat source problem is proved. We show that such a problem is mildly ill‐posed and further present two Tikhonov‐type regularization methods (a generalized Tikhonov regularization method and a simplified generalized Tikhonov regularization method) to deal with this problem. Convergence estimates are presented under the a priori choice of the regularization parameter. Numerical results are presented to illustrate the accuracy and efficiency of our methods. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
17.
Fractional (nonlocal) diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogs and they are used to model anomalous diffusion, especially in physics. In this paper, we study a backward problem for an inhomogeneous time-fractional diffusion equation with variable coefficients in a general bounded domain. Such a backward problem is of practically great importance because we often do not know the initial density of substance, but we can observe the density at a positive moment. The backward problem is ill-posed and we propose a regularizing scheme by using Tikhonov regularization method. We also prove the convergence rate for the regularized solution by using an a priori regularization parameter choice rule. Numerical examples illustrate applicability and high accuracy of the proposed method. 相似文献
18.
This paper deals with the inverse time problem for an axisymmetric heat equation. The problem is ill-posed. A modified Tikhonov regularization method is applied to formulate regularized solution which is stably convergent to the exact one. estimate between the approximate solution and exact technical inequality and improving a priori smoothness Meanwhile, a logarithmic-HSlder type error solution is obtained by introducing a rather assumption. 相似文献
19.