An application of Taylor models to the Nakao method on ODEs

DOI10.1007/BF03186540zbMath1185.65119MaRDI QIDQ849188

Nobito Yamamoto, Takashi Komori

Publication date: 25 February 2010

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jjiam/1265033787

zbMATH Keywords

numerical experimentsinitial value problemsTaylor modelvalidated computationNakao method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Algorithms with automatic result verification (65G20)

Uses Software

• Cosy

Cites Work

• Rigorously computed orbits of dynamical systems without the wrapping effect
• Efficient control of the dependency problem based on Taylor model methods
• Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY
• Verified integration of dynamics in the solar system.
• NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
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