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Numerical methods for inversion of the one-dimensional diffusion equation
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Numerical methods for inversion of the one-dimensional diffusion equation

Alexander Karlovitz
Master of Science (M.S.), Drexel University
Jun 2017
DOI:
https://doi.org/10.17918/etd-7407
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Abstract

Heat equation Inverse problems (Differential equations) Mathematics
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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