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Though an error analysis has already been given, a corresponding linear stability analysis is still lacking. We here provide such an analysis, together with some improvements concerning the mesh selection. This latter has been implemented into a new version of the code, which is available on the web.<\/jats:p>","DOI":"10.1007\/s10915-025-03006-9","type":"journal-article","created":{"date-parts":[[2025,7,28]],"date-time":"2025-07-28T04:49:36Z","timestamp":1753678176000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Analysis and implementation of collocation methods for fractional differential equations"],"prefix":"10.1007","volume":"104","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6290-4107","authenticated-orcid":false,"given":"Luigi","family":"Brugnano","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gianmarco","family":"Gurioli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Felice","family":"Iavernaro","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikk","family":"Vikerpuur","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,7,28]]},"reference":[{"key":"3006_CR1","doi-asserted-by":"publisher","first-page":"1489","DOI":"10.1007\/s11075-019-00733-7","volume":"83","author":"P Amodio","year":"2020","unstructured":"Amodio, P., Brugnano, L., Iavernaro, F.: Analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for the numerical solution of ODE problems. 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