Numerical treatment of ordinary differential equations by extrapolation methods

1966/03/01 by Roland Bulirsch, Josef Stoer · 852 citations
Mathematics · #Applied mathematics #Collocation method #Differential algebraic equation #Differential equation #Exponential integrator #Extrapolation #Mathematical analysis #Mathematics #Numerical analysis #Numerical methods for differential equations #Numerical methods for ordinary differential equations #Numerical stability #Ordinary differential equation #Runge–Kutta methods

paper · doi:10.1007/bf02165234

published in Numerische Mathematik 8(1), 1-13 (Springer Science+Business Media)

openalex publication_date 1966/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Cited by

• Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations
• The Drazin inverse in multibody system dynamics
• Dynamics of triple black hole systems in hierarchically merging massive galaxies
• Extreme Mass Ratio Inspirals triggered by Massive Black Hole Binaries: from Relativistic Dynamics to Cosmological Rates
• Reassessing the origin of Triton
• Fast and slow earthquakes emerge due to fault geometrical complexity
• Trajectory-based models in strong-field physics
• Reaction Dynamics for the [NNO] System from State-Resolved and Coarse-Grained Models
• Habitable-zone super-Earth candidate in a six-planet system around the K2.5V star HD 40307
• Stability and chaos in Kustaanheimo–Stiefel space induced by the Hopf fibration
• Finite element computation of the gravitational radiation emitted by a pointlike object orbiting a nonrotating black hole
• Bayesian analysis of the radial velocities of HD 11506 reveals another planetary companion
• Collisional Probability of Periodic Comets with the Terrestrial Planets: An Invalid Case of Analytic Formulation
• Level truncation and the quartic tachyon coupling
• Tidal evolution of the Uranian satellites
• Tidal heating of Ariel
• ORBITAL STRUCTURE OF MERGER REMNANTS. I. EFFECT OF GAS FRACTION IN PURE DISK MERGERS
• Numerical methods for ordinary differential equations in the 20th century
• Gravitational recoil from binary black hole mergers: The close-limit approximation
• Numerical quadrature by extrapolation
• Towards a theoretical determination of the geographical probability distribution of meteoroid impacts on Earth
• On the location of the ring around the dwarf planet Haumea
• Poincaré surfaces of section around a 3D irregular body: the case of asteroid 4179 Toutatis
• Multiple Stellar Evolution: a population synthesis algorithm to model the stellar, binary, and dynamical evolution of multiple-star systems
• A review of recent developments in solving ODEs
• Prediction of transits of Solar system objects inKepler/K2 images: an extension of the Virtual Observatory service SkyBoT
• ViSiON: Visibility Service for Observing Nights
• Correlation of macroscopic instability and Lyapunov times in the general three-body problem
• Extreme- and intermediate-mass ratio inspirals in dynamical Chern-Simons modified gravity
• The extrapolated explicit midpoint scheme for variable order and step size controlled integration of the Landau–Lifschitz–Gilbert equation
• Order and stepsize control in extrapolation methods
• Smoothing the extrapolated midpoint rule
• Simulating Highly Activated Sticking of H 2 on Al(110): Quantum versus Quasi-Classical Dynamics. [europepmc]
• Frustrated Synchronization of the Kuramoto Model on Complex Networks. [europepmc]