A dissertation submitted to the Faculty of Science, School of Mathematics
University of the Witwatersrand
Johannesburg
South Africa / Linear second order ordinary di erential boundary value problems feature prominently
in many scienti c eld, such as physics and engineering. Solving these problems
is often riddled with complications though a myriad of techniques have been
devised to alleviate these di culties. One such method is by transforming a problem
into a more readily solvable form or a problem which behaves in a manner which
is well understood. The Darboux-Crum transformation is a particularly interesting
transformation characterised by some surprising properties, and an increase in the
number of works produced in the last few years related to this transformation has
prompted this investigation. The classical orthogonal polynomials, namely those
of Jacobi, Legendre, Hermite and Laguerre, have been nominated as test candidates
and this work will investigate how these orthogonal families are a ected when
transformed via Darboux-Crum transformations.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/12928 |
| Date | 30 July 2013 |
| Creators | Rademeyer, Maryke Carleen |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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