| Summary: | 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.
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