Solving an Inverse Sturm-Liouville Problem by a Lie-Group Method. (7th February 2008)

• Record Type: Journal Article
• Authors: Liu, Chein-Shan
• Other Names: Rogers Colin Academic Editor.
• Is Part Of: Boundary value problems. Volume 2008(2008)
• Publication Date: 2008-02-07
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2008/749865
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we identify a Sturm-Liouville potential function by using the data of one eigenfunction and its corresponding eigenvalue, and identify a spatial-dependent unknown function of a Sturm-Liouville differential operator. The method we employ is to transform the inverse Sturm-Liouville problem into a parameter identification problem of a heat conduction equation. Then a Lie-group estimation method is developed to estimate the coefficients in a system of ordinary differential equations discretized from the heat conduction equation. Numerical tests confirm the accuracy and efficiency of present approach. Definite and random disturbances are also considered when comparing the present method with that by using a technique of numerical differentiation.