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Finite Extinction Time For Non-Linear Absorption-Diffusion Equations, Jacob B. Goldberg
Finite Extinction Time For Non-Linear Absorption-Diffusion Equations, Jacob B. Goldberg
Theses and Dissertations
In this thesis, we develop a numerical method in order to approximate the solutions of one-dimensional, non-linear absorption-diffusion equations. We test our method for accuracy against a linear diffusion equation with a solution that can be written in closed form. We then test various types of diffusion and absorption terms to determine which ones produce extinction in finite time. We also develop a numerical method to computationally solve diffusion-free equations. We compare the numerical solutions of the one-dimensional, non-linear absorption-diffusion equation and the diffusion-free equation and we find that for the cases tested, the numerical absorption-diffusion solutions are always less …