Some recent advances in validated methods for IVPs for ODEs

DOI10.1016/S0168-9274(01)00155-6zbMath0998.65068OpenAlexW2059261580MaRDI QIDQ1612462

Kenneth R. Jackson, Nedialko S. Nedialkov

Publication date: 22 August 2002

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(01)00155-6

zbMATH Keywords

stabilityerror boundsinitial value problemTaylor seriesinterval methodsQR algorithmsimultaneous iterationwrapping effectvalidated methodsHermite-Obreschkoff scheme

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) General methods in interval analysis (65G40) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Algorithms with automatic result verification (65G20)

Related Items

Dynamics of spatial rigid-flexible multibody systems with uncertain interval parameters, Validated solutions of initial value problems for parametric ODEs, Verified integration of linear \(n\)th order ODEs using large steps, On interval predictor-corrector methods, Interval methods of Adams-Bashforth type with variable step sizes, Interval versions of Milne's multistep methods, Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions, A polynomial chaos expansion approach for nonlinear dynamic systems with interval uncertainty, Interval versions for special kinds of explicit linear multistep methods, Status of the differential transformation method, Polynomial cost for solving IVP for high-index DAE, Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs, Numerical solutions of index-1 differential algebraic equations can be computed in polynomial time, Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information, Sparse regression Chebyshev polynomial interval method for nonlinear dynamic systems under uncertainty, Solving differential-algebraic equations by Taylor series. I: Computing Taylor coefficients

Uses Software

• FADBAD++
• TADIFF

Cites Work

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