2026-09-23T07:21:30Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/129534 2026-02-05 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

application/pdf en text Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-05-01 The student, Savana Ammons, accepted the attached license on 2025-04-15 at 23:41. The student, Savana Ammons, submitted this Dissertation for approval on 2025-04-16 at 00:04. This Dissertation was approved for publication on 2025-04-16 at 14:26. DSpace SAF Submission Ingestion Package generated from Vireo submission #21790 on 2025-10-19 at 19:14:58 The computation and semi-analytic theory of standing deep water waves Ammons, Savana Jade 2025-04-16 Hur, Vera Mikyoung Laugesen, Richard Bronski, Jared Tzirakis, Nikolaos Partial Differential Equations Differential Equations Water Waves Standing Waves Algorithms Numerical Analysis eng 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. 2025-05 Thesis https://hdl.handle.net/2142/129534 Copyright 2025 Savana Ammons Mathematics Mathematics University of Illinois Urbana-Champaign Ph.D. Dissertation