Validated and Numerically Efficient Chebyshev Spectral Methods for Linear Ordinary Differential Equations

DOI10.1145/3208103zbMath1484.65155OpenAlexW2739796060WikidataQ113310077 ScholiaQ113310077MaRDI QIDQ4611315

Nicolas Brisebarre, Florent Bréhard, Mioara Joldes

Publication date: 18 January 2019

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1145/3208103

zbMATH Keywords

linear ordinary differential equationsChebyshev seriesquasi-Newton methodspectral methodsD-finite functionsrigorous computingfixed-point validation

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

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A contour method for time-fractional PDEs and an application to fractional viscoelastic beam equations ⋮ A rigorous implicit \(C^1\) Chebyshev integrator for delay equations ⋮ Computing Semigroups with Error Control ⋮ A certificate-based approach to formally verified approximations ⋮ Enclosing Chebyshev Expansions in Linear Time ⋮ A symbolic-numeric validation algorithm for linear ODEs with Newton-Picard method

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