Computational uncertainty and the application of a high-performance multiple precision scheme to obtaining the correct reference solution of Lorenz equations

DOI10.1007/s11075-011-9481-6zbMath1232.65106OpenAlexW2103611281MaRDI QIDQ662893

Peng-fei Wang, Qian Li, Jian-ping Li

Publication date: 13 February 2012

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

Full work available at URL: https://doi.org/10.1007/s11075-011-9481-6

zbMATH Keywords

parallel computationLorenz equationsmultiple precisioncomputational uncertaintylong times solutionTaylor scheme

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (8)

On the risks of using double precision in numerical simulations of spatio-temporal chaos ⋮ Clean numerical simulation: a new strategy to obtain reliable solutions of chaotic dynamic systems ⋮ A database of rigorous and high-precision periodic orbits of the Lorenz model ⋮ Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system ⋮ Matlab Code for Lyapunov Exponents of Fractional-Order Systems ⋮ Can We Obtain a Reliable Convergent Chaotic Solution in any Given Finite Interval of Time? ⋮ Graphical Structure of Attraction Basins of Hidden Chaotic Attractors: The Rabinovich–Fabrikant System ⋮ Physical limit of prediction for chaotic motion of three-body problem

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Computational uncertainty principle in nonlinear ordinary differential equations. I. Numerical results
• Computational uncertainty principle in ordinary differential equations. II. Theoretical analysis
• Some Mathematical and Numerical Issues in Geophysical Fluid Dynamics and Climate Dynamics
• Deterministic Nonperiodic Flow

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