Keywords: Inverse coefficient problem (ICP) Lie-group adaptive method (LGAM) Leading coefficient Inverse Sturm–Liouville operator Iterative method a b s t r a c t We consider an inverse problem for identifying a leading coefficient a(x) in À(a(x)y 0 (x)) 0 + q(x)y(x) = H(x), which is known as an inverse coefficient problem for the Sturm–Liouville operator. We transform y(x) to u(x, t) = (1 + t)...

This paper deals with the discrete system being finite-difference approximation of Sturm–Liouville problem frozen argument. The inverse theory is developed for this system. We describe two principal cases: degenerate and non-degenerate. For these cases, appropriate problems statements are provided, uniqueness theorems proved, reconstruction algorithms obtained. Moreover, relationship between ei...