| In this research, I derive a refined asymptotic expression for the eigenvalues, lnn ∈Z , of the operator matrix from the telegrapher's equation to accuracy O(1/n²). First, the expression for the "shooting function" is refined to O(1/n²) using a "fake potential" and a Neumann series. Then, this expression for the "shooting function" is used to refine the expressions for the eigenvalues. This refinement of the previously published results of accuracy O(1/| n|) enables the inverse spectral problem (recovering unknown resistance) to be solved in numerical experiments, using Fourier series. One application of this recovery process would be to find a fault in the insulation of a submarine telegraph cable without having to physically inspect every inch of the cable. |
