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≡−(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.