A step-size selection strategy for explicit Runge-Kutta methods based on Lyapunov exponent theory

DOI10.1016/j.cam.2015.03.056zbMath1329.65154OpenAlexW1977603738MaRDI QIDQ495103

Andrew J. Steyer, Erik S. Van Vleck

Publication date: 9 September 2015

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

Full work available at URL: https://doi.org/10.1016/j.cam.2015.03.056

zbMATH Keywords

Lyapunov exponentsRunge-Kutta methodsnumerical stability analysisstep-size selection

Mathematics Subject Classification ID

Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Topological dynamics of nonautonomous systems (37B55)

Related Items (3)

Underlying one-step methods and nonautonomous stability of general linear methods ⋮ A Very Simple Method to Calculate the (Positive) Largest Lyapunov Exponent Using Interval Extensions ⋮ On the use of interval extensions to estimate the largest Lyapunov exponent from chaotic data

Cites Work

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• Perturbation theory for approximation of Lyapunov exponents by QR methods
• A 3(2) pair of Runge-Kutta formulas
• Linear and non-linear stability for general linear methods
• The equivalence of algebraic stability and AN-stability
• A PI stepsize control for the numerical solution of ordinary differential equations
• Stability of explicit time discretizations for solving initial value problems
• On the behaviour of global errors at infinity in the numerical integration of stable initial value problems
• Dichotomies in stability theory
• On the error in computing Lyapunov exponents by QR methods
• Lyapunov and Sacker-Sell spectral intervals
• Accurate Computations on Inertial Manifolds
• G-stability is equivalent toA-stability
• On the Error in the Product QR Decomposition
• Solving Ordinary Differential Equations I
• Convergence and stability in the numerical integration of ordinary differential equations
• On the Error in QR Integration
• Global lyapunov exponents, kaplan-yorke formulas and the dimension of the attractors for 2D navier-stokes equations
• Equilibrium states of Runge Kutta schemes
• Equilibrium states of Runge-Kutta schemes: part II
• Contractive methods for stiff differential equations part I
• Contractive methods for stiff differential equations Part II
• THE DYNAMICS OF RUNGE–KUTTA METHODS
• Lyapunov Spectral Intervals: Theory and Computation
• Solving Ordinary Differential Equations II
• A unified approach to compute foliations, inertial manifolds, and tracking solutions
• Some Numerical Aspects of Computing Inertial Manifolds

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