Solution of an inverse coefficient problem for an ordinary differential equation

Abstract

In this paper inverse coefficient problems related to the Sturm-Liouville equation-(k(x)u^')^' + q(x)u = f (x) are considered. The unknown coefficient k = k(x) is required to belong to a set of admissible coefficients K_:0 which is compact in H¹. For the corresponding direct problem a stability estimate in C^0,λ-norm, is derived and existence theorems for quasisolutions of certain inverse problems are proved. Numerical algorithms and numerical results for some examples are described

Keywords:

• inverse coefficient problem
• ordinary differential equation
• quasisolution
• coefficient stability