Travelling waves for the spatially discretized bistable Allen-Cahn equation
M. Verton (TU Delft - Electrical Engineering, Mathematics and Computer Science)
W.M. Schouten-Straatman – Mentor (TU Delft - Mathematical Physics)
Fokko van de Bult – Graduation committee member (TU Delft - Analysis)
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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.