Global, rigorous and realistic bounds for the solution of dissipative differential equations. I: Theory

DOI10.1007/BF02276880zbMath0809.65077MaRDI QIDQ1332684

Arnold Neumaier, Murray Hill

Publication date: 1 September 1994

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

interval analysiserror boundsdifferential inequalitieslogarithmic normsdissipative differential equations

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Interval and finite arithmetic (65G30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (3)

Error bounds for initial value problems by optimization ⋮ Certified error bounds for uncertain elliptic equations ⋮ Some recent advances in validated methods for IVPs for ODEs

Cites Work

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• Norm bounds for rational matrix functions
• On the stability of semi-implicit methods for ordinary differential equations
• A basic theorem in the computation of ellipsoidal error bounds
• A New Modified Cholesky Factorization
• Interval Slopes for Rational Functions and Associated Centered Forms
• Interval Methods for Systems of Equations
• On Logarithmic Norms

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