Determination of leading coefficients in Sturm-Liouville operator from boundary measurements. II: Unicity and an engineering approach.
[ For part I see ibid. 125, 1--21 (2002; Zbl 1032.65078).] The authors present a scheme to determine the leading coefficient \(k(x)\) of the Sturm-Liouville operator \(Au(x) \equiv -(k(x)u'(x))'+q(x)u(x)\), \(x \in (a, b)\), with measured data given in the form of Dirichlet/Neumann type boundary conditions. The problem is reduced to a Cauchy problem for a first-order ordinary differential equation with respect to \(k(x)\). An analytical formula is presented for an approximate solution of the inverse problem. Numerical examples related to the accuracy of the solution and to essential features of the inverse problem are presented.
scientific article; zbMATH DE number 1860978