A class of multistep numerical difference schemes applied in inverse heat conduction problem with a control parameter. Issue 7 (3rd July 2019)

• Record Type: Journal Article
• Authors: Zhang, Yong-Fu; Li, Chong-Jun
• Is Part Of: Inverse problems in science and engineering. Volume 27:Issue 7(2019)
• Page Start: 887
• Page End: 942
• Publication Date: 2019-07-03
• Subjects: Inverse heat conduction problem -- Tikhonov regularization method -- numerical difference schemes -- linear multistep method -- Lagrange interpolation; 65N21 -- 65L06 -- 65D05; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2018.1501370
• Languages: English
• ISSNs: 1741-5977

Abstract

ABSTRACT: As this paper is concerned with a class of multistep numerical difference techniques to solve one-dimensional parabolic inverse problems with source control parameter p ( t ), we apply the linear multistep method combining with Lagrange interpolation to develop three different numerical difference schemes. The problem of numerical differentiation with noisy scattered data is mildly ill-posed, the smoothing spline model based on Tikhonov regularization method is developed to compute numerical derivative contaminated by noise error. Simultaneously, the truncation error estimations and the convergence conclusions are proposed for the above difference methods respectively. The results of numerical tests with different noise levels are given to show that the presented algorithms are accurate and effective.