Travelling waves for the spatially discretized bistable Allen-Cahn equation

Bachelor thesis (2023)

Authors

M. Verton Electrical Engineering, Mathematics and Computer Science

Contributors

W.M. Schouten-Straatman Mathematical Physics - EEMCS (mentor)
F.J. van de Bult Analysis - EEMCS (graduation committee member)
Faculty
Electrical Engineering, Mathematics and Computer Science, Electrical Engineering, Mathematics and Computer Science
Copyright: © 2023 Max Verton
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Published Date

07-07-2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

We analyze the spatially discretized version of the Allen-Cahn partial differential equation. The second order derivative is numerically approximated by a weighted infinite sum. The coefficients of this sum as well as the function f in the differential equation have got freedom inside determined restrictions. For this spatially discretized variation of the Allen-Cahn partial differential equation, we prove the existence of a travelling wave solution.