University of Illinois Urbana-Champaign

The computation and semi-analytic theory of standing deep water waves

Ammons, Savana Jade

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https://hdl.handle.net/2142/129534

Description

Title
The computation and semi-analytic theory of standing deep water waves
Author(s)
Ammons, Savana Jade
Issue Date
2025-04-16
Director of Research (if dissertation) or Advisor (if thesis)
Hur, Vera Mikyoung
Doctoral Committee Chair(s)
Laugesen, Richard
Committee Member(s)
  • Bronski, Jared
  • Tzirakis, Nikolaos
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Partial Differential Equations
  • Differential Equations
  • Water Waves
  • Standing Waves
  • Algorithms
  • Numerical Analysis
Abstract
We implement a modified version of the algorithm created by Amick and Toland to numerically compute the coefficients of the power series solutions to the classical standing water wave problem. With this algorithm, we precisely compute the coefficients to the 39th order of the wave amplitude. We also verify that Amick and Toland's algorithm is equivalent to Schwartz and Whitney's. We are unable to prove that the resulting power series solutions converge, although we propose a proof technique involving rigorous numerics and classical induction that may work for simpler problems. In lieu of a convergence proof, we estimate the solutions' radius of convergence, in the event that they do converge, using both truncated Taylor series and Pad\'e approximants. Additionally, we conjecture about the solutions' local behavior and analytic structure.
Graduation Semester
2025-05
Type of Resource
Thesis
Handle URL
https://hdl.handle.net/2142/129534
Copyright and License Information
Copyright 2025 Savana Ammons

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