{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/129534"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/129534","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The computation and semi-analytic theory of standing deep water waves","abstract":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-05-01","abstract_html":"Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-05-01","abstract_has_math":false,"creators":["Ammons, Savana Jade"],"institution":"University of Illinois Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Hur, Vera Mikyoung","Laugesen, Richard","Bronski, Jared","Tzirakis, Nikolaos"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-04-16","date_published":"2025-04-16","updated_at":"2026-07-22T22:25:05Z","subjects":["Partial Differential Equations","Differential Equations","Water Waves","Standing Waves","Algorithms","Numerical Analysis"],"languages":["en","eng"],"rights":["Copyright 2025 Savana Ammons"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/129534","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hur, Vera Mikyoung","Laugesen, Richard","Bronski, Jared","Tzirakis, Nikolaos"]},{"key":"dc:creator","label":"Author","values":["Ammons, Savana Jade"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-04-16","2025-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Partial Differential Equations","Differential Equations","Water Waves","Standing Waves","Algorithms","Numerical Analysis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2025 Savana Ammons"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/129534"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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","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."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The computation and semi-analytic theory of standing deep water waves"]}]}],"canonical_facts":{"dc:contributor":["Hur, Vera Mikyoung","Laugesen, Richard","Bronski, Jared","Tzirakis, Nikolaos"],"dc:creator":["Ammons, Savana Jade"],"dc:date":["2025-04-16","2025-05"],"dc:description":["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","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."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/129534"],"dc:language":["en","eng"],"dc:rights":["Copyright 2025 Savana Ammons"],"dc:subject":["Partial Differential Equations","Differential Equations","Water Waves","Standing Waves","Algorithms","Numerical Analysis"],"dc:title":["The computation and semi-analytic theory of standing deep water waves"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:05Z"}