[2004.02604] Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2004.02604 (math) [Submitted on 2 Apr 2020 ( v1 ), last revised 25 Apr 2026 (this version, v2)] Title: Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis Authors: Emmanuel Roque , José A Vallejo View a PDF of the paper titled Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis, by Emmanuel Roque and Jos\'e A Vallejo View PDF HTML (experimental) Abstract: We provide the details of an implementation of Fourier techniques for solving second-order linear partial differential equations (with constant coefficients) using a computer algebra system. The general Sturm-Liouville problem for the heat, wave and Laplace operators on the most common bounded domains is covered, as well as the general second-order linear parabolic equation with constant coefficients, which includes cases such as the convection-diffusion equation, by reduction to the heat equation. Comments: Second version. 22 pages, 6 figures Subjects: Numerical Analysis (math.NA) MSC classes: 35-04, 35C10:65T40 Cite as: arXiv:2004.02604 [math.NA] (or arXiv:2004.02604v2 [math.NA] for this version) https://doi.org/10.48550/arXiv.2004.02604 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Emmanuel Roque [ view email ] [v1] Thu, 2 Apr 2020 10:53:41 UTC (149 KB) [v2] Sat, 25 Apr 2026 21:08:31 UTC (280 KB) Full-text links: Access Paper: View a PDF of the paper titled Automated solving of constant-coefficients second-order linear PDEs using Fourier analysis, by Emmanuel Roque and Jos\'e A Vallejo View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2020-04 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from