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

Alemder Hasanov and Burhan Pektas

Mathematics and Computers in Simulation (MATCOM), 2002, vol. 61, issue 1, 47-52

Abstract: 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.

Keywords: Inverse coefficient problem; Ill-conditioned situations; Polynomial approximation (search for similar items in EconPapers)
Date: 2002
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