Verified integration of linear \(n\)th order ODEs using large steps

DOI10.1016/j.amc.2006.08.033zbMath1114.65082OpenAlexW2085058560MaRDI QIDQ876676

Markus Neher

Publication date: 26 April 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.08.033

zbMATH Keywords

numerical examplesinterval analysiserror boundspower seriesenclosure methodinterval computationsroundoff errorsTaylor polynomial

Mathematics Subject Classification ID

General methods in interval analysis (65G40) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items

A note on a sum associated with the generalized hypergeometric function

Uses Software

• ACETAF
• PASCAL-XSC

Cites Work

• A note on a sum associated with the generalized hypergeometric function
• Derived eigenvalues of symmetric matrices, with applications to distance geometry
• Survey of integral algorithms for ordinary differential equations
• Rigorously computed orbits of dynamical systems without the wrapping effect
• Verified integration of ODEs and flows using differential algebraic methods on high-order Taylor models
• An effective high-order interval method for validating existence and uniqueness of the solution of an IVP for an ODE
• Some recent advances in validated methods for IVPs for ODEs
• Validated solutions of initial value problems for ordinary differential equations
• Improved validated bounds for Taylor coefficients and for Taylor remainder series
• An enclosure method for the solution of linear odes with polynomial coefficients
• Numerical Software with Result Verification
• ACETAF
• Validated bounds for Taylor coefficients of analytic functions
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