Reducing rounding errors and achieving Brouwer's law with Taylor series method

DOI10.1016/j.apnum.2012.03.008zbMath1243.65080OpenAlexW2087127050MaRDI QIDQ425370

Marcos Rodríguez, Roberto Barrio

Publication date: 8 June 2012

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2012.03.008

zbMATH Keywords

performancenumerical examplesefficiencydynamical systemTaylor series methodrounding errorBrouwer's lawcompensated Horner algorithmKahan summation algorithmlong term integration

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) Error bounds for numerical methods for ordinary differential equations (65L70) Complexity and performance of numerical algorithms (65Y20)

Related Items (3)

Tuning Symplectic Integrators is Easy and Worthwhile ⋮ OpenCL parallel integration of ordinary differential equations: applications in computational dynamics ⋮ Automatic implementation of the numerical Taylor series method: a \textsc{Mathematica} and \textsc{Sage} approach

Uses Software

• mctoolbox
• TIDES
• ATOMFT
• Taylor

Cites Work

• VSVO formulation of the Taylor method for the numerical solution of ODEs
• Algorithms for accurate, validated and fast polynomial evaluation
• Reducing round-off errors in rigid body dynamics
• Achieving Brouwer's law with implicit Runge-Kutta methods
• Numerical implementation of the exact dynamics of free rigid bodies
• Accurate simple zeros of polynomials in floating point arithmetic
• Choosing a stepsize for Taylor series methods for solving ODE'S
• ATOMFT: Solving ODEs and DAEs using Taylor series
• Performance of the Taylor series method for ODEs/DAEs
• Polynomial cost for solving IVP for high-index DAE
• A Software Package for the Numerical Integration of ODEs by Means of High-Order Taylor Methods
• Solving Ordinary Differential Equations Using Taylor Series
• Accuracy and Stability of Numerical Algorithms
• Sensitivity Analysis of ODES/DAES Using the Taylor Series Method
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