Picard iteration-based variable-order integrator with dense output employing algorithmic differentiation

DOI10.1007/s11075-018-0489-zzbMath1434.65090OpenAlexW2792624595MaRDI QIDQ1717573

Afnan Al Marzouk, Herman D. Schaumburg, Bela Erdelyi

Publication date: 7 February 2019

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-018-0489-z

zbMATH Keywords

algorithmic differentiationvariable orderdense outputPicard iteration-based

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) (n)-body problems (70F10) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Uses Software

• Cosy
• ATOMFT
• Taylor
• NBODY4

Cites Work

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• Differential equations and their applications. An introduction to applied mathematics. 3rd ed
• The global solution of the n-body problem
• ATOMFT: Solving ODEs and DAEs using Taylor series
• An adaptive \(N\)-body algorithm of optimal order.
• Automatic differentiation: Applications, theory, and implementations. Selected papers based on the presentation at the 4th international conference on automatic differentiation (AD), Chicago, IL, USA, July 20--23, 2004
• Solving Ordinary Differential Equations I
• A Software Package for the Numerical Integration of ODEs by Means of High-Order Taylor Methods
• The Curious History of Faa di Bruno's Formula
• Gravitational N-Body Simulations
• A special stability problem for linear multistep methods

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