Projection methods preserving Lyapunov functions

DOI10.1007/s10543-010-0259-3zbMath1194.65090OpenAlexW1995213327MaRDI QIDQ981671

Manuel Calvo, M. P. Laburta, Luis Rández, Juan I. Montijano

Publication date: 2 July 2010

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-010-0259-3

zbMATH Keywords

Lyapunov functionnumerical experimentsinitial value problemsGaussian quadratureprojection methodsexplicit Runge-Kutta methodsgeometric numerical integration

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (17)

Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian differential equations ⋮ Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs ⋮ Projected Runge-Kutta methods for constrained Hamiltonian systems ⋮ Numerical methods for non conservative perturbations of conservative problems ⋮ High-order supplementary variable methods for thermodynamically consistent partial differential equations ⋮ A modified Runge-Kutta method for increasing stability properties ⋮ General relaxation methods for initial-value problems with application to multistep schemes ⋮ Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation ⋮ Supplementary variable method for thermodynamically consistent partial differential equations ⋮ Runge-Kutta projection methods with low dispersion and dissipation errors ⋮ Invariants preserving schemes based on explicit Runge-Kutta methods ⋮ Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms ⋮ Exponential Integrators Preserving First Integrals or Lyapunov Functions for Conservative or Dissipative Systems ⋮ Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations ⋮ Energy Stability of Explicit Runge--Kutta Methods for Nonautonomous or Nonlinear Problems ⋮ Exponential collocation methods for conservative or dissipative systems ⋮ Relaxation Runge-Kutta methods for Hamiltonian problems

Uses Software

• Matlab
• ode23
• ode45
• Ode15s
• ode113
• ode23s
• MATLAB ODE suite

Cites Work

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• Stability theory by Liapunov's direct method
• Geometric integration methods that preserve Lyapunov functions
• The MATLAB ODE Suite
• Solving Ordinary Differential Equations I
• Simulating Hamiltonian Dynamics
• Splitting methods
• On the Preservation of Invariants by Explicit Runge--Kutta Methods
• Interpolation for Runge–Kutta Methods
• Derivation of Efficient, Continuous, Explicit Runge–Kutta Methods
• Geometric integration: numerical solution of differential equations on manifolds
• Geometric integration using discrete gradients
• The Global Dynamics of Discrete Semilinear Parabolic Equations
• Unified Approach to Hamiltonian Systems, Poisson Systems, Gradient Systems, and Systems with Lyapunov Functions or First Integrals
• Interpolants for Runge-Kutta formulas
• Geometric integrators for ODEs

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