A new method for numerical differentiation based on direct and inverse problems of partial differential equations. (May 2015)

• Record Type: Journal Article
• Authors: Wang, Zewen; Wang, Haibing; Qiu, Shufang
• Is Part Of: Applied mathematics letters. Volume 43(2015:May)
• Page Start: 61
• Page End: 67
• Publication Date: 2015-05
• Subjects: Numerical differentiation -- Ill-posed problem -- Inverse source -- PDEs-based method; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2014.11.016
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we mainly study a numerical differentiation problem which aims to approximate the second order derivative of a single variable function from its noise data. By transforming the problem into a combination of direct and inverse problems of partial differential equations (heat conduction equations), a new method that we call the PDEs-based numerical differentiation method is proposed. By means of the finite element method and the Tikhonov regularization, implementations of the proposed PDEs-based method are presented with a posterior strategy for choosing regularization parameters. Numerical results show that the PDEs-based numerical differentiation method is highly feasible and stable with respect to data noise.