Chu-Li Fu

A modified method for a backward heat conduction problem

We consider a backward heat conduction problem in a strip, where data is given at the final time t = T(T > 0) and a solution for 0 <= t < T is sought. The problem is ill-posed in the sense that the solution(if it exists) does not depend continuously on the data. In order to numerically solve the problem, we study a modification of the equation, where a third-order mixed derivative term is added. Error estimates for this problem are given, which show that the modified problem is stable and its solution is an approximation of the backward heat conduction problem. Some numerical tests illustrate that the proposed method is feasible and effective. (c) 2006 Elsevier Inc. All rights reserved.

The method of simplified Tikhonov regularization for dealing with the inverse time-dependent heat source problem

This paper investigates the inverse problem of determining a heat source using a parabolic equation where data are given at some fixed location. The problem is ill-posed, i.e., the solution (if it exists) does not depend continuously on the data. A simplified Tikhonov regularization method is given and an order optimal stability estimate is obtained. A numerical example shows that the regularization method is effective and stable.

Regularization strategies for a two-dimensional inverse heat conduction problem

We consider a two-dimensional inverse heat conduction problem for a slab. This is a severely ill-posed problem. Two regularization strategies, one based on the modification of the equation, the other based on the truncation of high frequency components, are proposed to solve the problem in the presence of noisy data. Error estimates show that the regularized solution is dependent continuously on the data and is an approximation of the exact solution of the two-dimensional inverse heat conduction problem. The relation of these two and other regularization strategies is also discussed.

Fourier regularization method for solving a Cauchy problem for the Laplace equation

In this article, we use Fourier method to solve a Cauchy problem for the Laplace equation in a strip region, the method is rather simple and convenient. Meanwhile, we overstep the Hölder continuity and provide some more sharp error estimates between the exact solution and its approximation. Numerical examples also show that the method work effectively.

A simple regularization method for stable analytic continuation

The problems of analytic continuation are frequently encountered in many practical applications. These problems are well known to be severely ill-posed and therefore several regularization methods have been suggested for solving them. In this paper we consider the problem of analytic continuation of the analytic function f(z) = f(x + iy) on a strip domain , where the data are given only on the line y = 0. We use a very simple and convenient method—the Fourier regularization method to solve this problem. Some sharp error estimates between the exact solution and its approximation are given and numerical examples show the method works effectively.

Two numerical methods for solving a backward heat conduction problem

We introduce a central difference method and a quasi-reversibility method for solving a backward heat conduction problem (BHCP) numerically. For these two numerical methods, we give the stability analysis. Meanwhile, we investigate the roles of regularization parameters in these two methods. Numerical results show that our algorithm is effective.

Numerical approximation of solution of nonhomogeneous backward heat conduction problem in bounded region

In this paper we consider a numerical approximation of solution of nonhomogeneous backward heat conduction problem (BHCP) in bounded region based on Tikhonov regularization method. Error estimate at t=0 for this method is provided. According to the error estimate, a selection of regularization parameter is given. Meanwhile, a numerical implementation is described and the numerical results show that our algorithm is effective.

A modified Tikhonov regularization method for a spherically symmetric three-dimensional inverse heat conduction problem

This paper deals with a spherically symmetric three-dimensional inverse heat conduction problem of determining the internal surface temperature distribution of a hollow sphere from the measured data at a fixed location inside it. This is an ill-posed problem, i.e., the solution (if it exists) does not depend continuously on the data. A modified Tikhonov regularization method is given and an order optimal stability estimate is obtained.

Wavelets and regularization of the sideways heat equation

In this paper, the following inverse heat conduction problem: ut = uxx,x≥0,t≥0, u(x,0) = 0,x≥0 u(1,t) = g(t),t≥0, u|x→∞ is bounded, is considered again. This problem is severely ill-posed: its solution (if it exists) does not depend continuously on the data; a small perturbation in the data may cause a dramatically large error in the solution for 0 < x < 1. In this paper, a new wavelet regularization method for this problem is given. Moreover, we can easily find the regularization parameter J such that some sharp stable estimates between the exact solution and the approximate one in Hr(R)-norm meaning is given.

Source term identification for an axisymmetric inverse heat conduction problem

We consider an inverse heat source problem of determining the heat source term from the final temperature history of a cylinder. This problem is ill-posed. A simplified Tikhonov regularization method is applied to formulate regularized solution, which is stably convergent to the exact one with a logarithmic type error estimate.