Reconstructing a second-order Sturm–Liouville operator by an energetic boundary function iterative method. (November 2017)

• Record Type: Journal Article
• Authors: Liu, Chein-Shan; Li, Botong
• Is Part Of: Applied mathematics letters. Volume 73(2017:Nov.)
• Page Start: 49
• Page End: 55
• Publication Date: 2017-11
• Subjects: Inverse coefficient problem -- Potential function -- Inverse Sturm–Liouville operator -- Energetic boundary function method -- Iterative method; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2017.04.023
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We consider an inverse problem for reconstructing the second-order Sturm–Liouville operator with the help of boundary data. The concept of energetic boundary functions, which satisfy the given boundary conditions and preserve the energy, is introduced for the first time. Then, we can derive a linear system to recover the unknown important coefficients of leading coefficient and potential function through a few iterations. Two examples are given to verify the iterative method.