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.
| Identifer | oai:union.ndltd.org:RICE/oai:scholarship.rice.edu:1911/70278 |
| Date | January 2011 |
| Contributors | Cox, Steven |
| Source Sets | Rice University |
| Language | English |
| Detected Language | English |
| Type | Thesis, Text |
| Format | 97 p., application/pdf |
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