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In this paper a simple and convenient new regularization method for solving backward heat equation— Fourier regularization method is given. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively. © 2006 Elsevier Inc. All rights reserved.

- Xiang-Tuan Xiong, Chu-Li Fu, Zhi Qian, Xiang Gao
- Int. J. Math. Mathematical Sciences
- 2006

The backward heat conduction problem (BHCP) is also referred to as the final boundary value problem. In general no solution which satisfies the heat conduction equation with final data and the boundary conditions exists. Even if a solution exists, it will not be continuously dependent on the final data. The BHCP is a typical example of an illposed problem… (More)

- Xiang-Tuan Xiong, Chu-Li Fu, +4 authors Zhi Qian
- 2007

We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective.

- Zhi Qian, Chu-Li Fu, Xiang-Tuan Xiong, Ting Wei
- Applied Mathematics and Computation
- 2006

We consider a classical ill-posed problem—numerical differentiation with a new method. We propose Fourier truncation method to compute high order numerical derivatives. A Hölder-type stability estimate is obtained. A numerical implementation is described. Numerical examples show that the proposed method is effective and stable. 2006 Elsevier Inc. All rights… (More)

- Xiang-Tuan Xiong
- J. Computational Applied Mathematics
- 2010

We investigate a Cauchyproblem for theHelmholtz equation. Amodified boundarymethod 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. © 2009 Elsevier B.V. All rights reserved.

- Chu-Li Fu, Xiang-Tuan Xiong, Peng Fu
- Mathematical and Computer Modelling
- 2005

- Xiang-Tuan Xiong, Chu-Li Fu
- Applied Mathematics and Computation
- 2006

In this paper, we consider the Cauchy problem for the Laplace’s equation where the Cauchy data is given at x = 0 and the solution is sought in the interval 0 < x < 1. A semi-discrete difference schemes together with a choice of regularization parameter is presented and error estimate is obtained. A numerical example shows that the method works effectively.… (More)

- Ai-Lin Qian, Xiang-Tuan Xiong, Yu-Jiang Wu
- J. Computational Applied Mathematics
- 2010

- Xiang-Tuan Xiong, Chu-Li Fu, Zhi Qian
- Applied Mathematics and Computation
- 2006

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. 2005… (More)

- Zhi Qian, Chu-Li Fu, Xiang-Tuan Xiong
- Applied Mathematics and Computation
- 2006