Refined Spectral Asymptotics for the Telegrapher's Equation
Cox, Steven J.
Master of Arts
In this research, I derive a refined asymptotic expression for the eigenvalues, [Special characters omitted.] , of the operator matrix from the telegrapher's equation to accuracy O (1/ n 2). First, the expression for the "shooting function" is refined to O (1/ n 2) 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.
Applied sciences; Applied mathematics