Simulation of ill-conditioned situations in inverse coefficient problem for the Sturm-Liouville operator based on boundary measurements

The problem of determining the unknown coefficient k = k(x) of the Sturm-Liouville operator Au equivalent to -(k(x)u' (x))' + q(x)u(x) from the measured data at the boundary x = 0; 1 is considered. It is assumed that the function u = u(x) has several singular points in (0, 1) of different types. As a result different types of ill-conditioned situations (mild, moderate and severe) in (0, 1) arise. We analyze all the ill-conditioned situations and then based on the analysis construct computational method for the solution of the inverse problem. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.