Reconstructing a second-order Sturm-Liouville operator by an energetic boundary function iterative method

We consider an inverse problem for reconstructing the second-order Sturm-Liouville operator with the help of boundary data. The concept of energetic boundary functions, which satisfy the given boundary conditions and preserve the energy, is introduced for the first time. Then, we can derive a linear system to recover the unknown important coefficients of leading coefficient and potential function through a few iterations. Two examples are given to verify the iterative method.