Inverse eigenvalue problem

• Main Author: Boamah, Edward Kwasi
• Format: Others
• Language: en
• Published: 2016
• Subjects: Matrices.; Eigenvalues
• Online Access: http://hdl.handle.net/10539/20865

A RESEARCH REPORT submitted to the Faculty of Science of the University of the Witwatersrand in partial fulfilment of the degree of MASTER OF SCIENCE Johannesburg, Republic of South Africa December1998· === This work is concerned with the Inverse Eigenvalue Problem for ordinary differential equations of the Sturm-Liouville type in the general form --dd ( 7' ()xdll(t\,:rI)) + {(q) x - t\p:(r )} u (A, Xl, = 0, .1' c.r (I :::: .7' S; b. The central problem considered ill this research is the approximate reC011- struction of the unknown coefficient function q(:l') in the Sturm-Liouville equation JOIl Irom a given finite spectral data set ~i(q), for i = 1 : n . A solution is sought using a finite element discretization method. The method works br solving the non-Iinear system arising out of the difference between the eigenvalues A,(q) of the Sturm-Liouville differential equation and the given spectral data ~i(q). Numerical results me presented to illustrate the effectiveness of the discretization method ill question.