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These examples show that the Laplace transform solution is very reliable for linear retarded delay-differential equations, because the analytic solution, for a single delta function input, is continuous. However, for linear neutral delay-differential equations with a delta function input the analytic solution is discontinuous. Consequently, the well-known Gibbs phenomenon is observed in the vicinity of the discontinuities. However, for neutral delay differential equations, we show that in some cases, the magnitude of the jumps at the discontinuities decrease, as time increases. Therefore, the Gibbs phenomenon of the Laplace solution dissipates.<\/jats:p>","DOI":"10.1007\/s40314-023-02405-8","type":"journal-article","created":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T14:02:20Z","timestamp":1690984940000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Analytical solutions of linear delay-differential equations with Dirac delta function inputs using the Laplace transform"],"prefix":"10.1007","volume":"42","author":[{"given":"Michelle","family":"Sherman","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gilbert","family":"Kerr","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5847-678X","authenticated-orcid":false,"given":"Gilberto","family":"Gonz\u00e1lez-Parra","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,8,2]]},"reference":[{"issue":"2","key":"2405_CR1","first-page":"714","volume":"203","author":"A Abdi","year":"2008","unstructured":"Abdi A, Hosseini SM (2008) An investigation of resolution of 2-variate Gibbs phenomenon. 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