{"title":"Solving a Delay Differential Equation through Fourier Transform","authors":"Kenta Ohira, Toru Ohira","doi":"arxiv-2401.02027","DOIUrl":null,"url":null,"abstract":"In this study, we introduce and explore a delay differential equation that\nlends itself to explicit solutions in the Fourier-transformed space. Through\nthe careful alignment of the initial function, we can construct a highly\naccurate solution to the equation. These findings open new avenues for\nunderstanding delay systems, demonstrating the efficacy of Fourier transform\ntechniques in capturing transient oscillatory dynamics.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"23 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Adaptation and Self-Organizing Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2401.02027","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, we introduce and explore a delay differential equation that
lends itself to explicit solutions in the Fourier-transformed space. Through
the careful alignment of the initial function, we can construct a highly
accurate solution to the equation. These findings open new avenues for
understanding delay systems, demonstrating the efficacy of Fourier transform
techniques in capturing transient oscillatory dynamics.
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