Thesis
Numerical methods for inversion of the one-dimensional diffusion equation
Master of Science (M.S.), Drexel University
Jun 2017
DOI:
https://doi.org/10.17918/etd-7407
Abstract
The one-dimensional diffusion equation comes up in a variety of physical circumstances. Both analytical and numerical methods are well understood for the forward problem. However, methods for the inversion of this equation remain of interest in the mathematical community. In this paper, two novel inversion methods are presented, along with preliminary results from testing. The first method involves heavy use of the Lanczos Method, an algorithm which converts a basis into an orthonormal basis with some other useful properties. The second involves a direct linearization of the equation before numerical inversion.
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Details
- Title
- Numerical methods for inversion of the one-dimensional diffusion equation
- Creators
- Alexander Karlovitz - DU
- Contributors
- Shari Moskow (Advisor) - Drexel University (1970-)
- Awarding Institution
- Drexel University
- Degree Awarded
- Master of Science (M.S.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- v, 21 pages
- Resource Type
- Thesis
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 7407; 991014632173204721