A truncated Legendre spectral method for solving numerical differentiation

Abstract

A numerical differentiation problem for a given function with noisy data is discussed in this paper. A truncated spectral method has been introduced to deal with the ill-posedness of the problem. The theoretical analysis shows that the smoother the genuine solution, the higher the convergence rate of the numerical solution by our method. Numerical examples are also given to show the efficiency of the method.

Keywords:

• numerical differentiation
• ill-posed problem
• truncated Legendre spectral method
• regularization method

2000 AMS Subject Classifications :

• 65D25
• 47A52

Acknowledgements

The author wishes to thank the editor and the referees for their very constructive comments and suggestions, which led to the present improved version of our paper. This work is supported by the Science Foundation of Guangdong Ocean University (No. 0812279).