On the positivity step size threshold of Runge--Kutta methods

DOI10.1016/j.apnum.2004.08.026zbMath1073.65077OpenAlexW2064890304MaRDI QIDQ1772804

Zoltán Horváth

Publication date: 21 April 2005

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2004.08.026

zbMATH Keywords

initial value problemRunge-Kutta methodinvariant conegeneralized positivity

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

Positive and elementary stable explicit nonstandard Runge-Kutta methods for a class of autonomous dynamical systems ⋮ On the optimal CFL number of SSP methods for hyperbolic problems ⋮ Invariance preserving discretization methods of dynamical systems ⋮ High order strong stability preserving time discretizations ⋮ Positively invariant cones of dynamical systems under Runge-Kutta and Rosenbrock-type discretization ⋮ A comprehensive theory on generalized BBKS schemes ⋮ Numerical integration of positive linear differential-algebraic systems ⋮ Strong stability for Runge-Kutta schemes on a class of nonlinear problems ⋮ Extension of modified Patankar-Runge-Kutta schemes to nonautonomous production-destruction systems based on Oliver's approach ⋮ A novel unified approach to invariance conditions for a linear dynamical system ⋮ Optimal monotonicity-preserving perturbations of a given Runge-Kutta method ⋮ On stability issues for IMEX schemes applied to 1D scalar hyperbolic equations with stiff reaction terms ⋮ Research of Precise Time Integration Method and its Derived Formats on Helicopter Rotor Dynamics ⋮ Steplength thresholds for invariance preserving of discretization methods of dynamical systems on a polyhedron

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the positivity of matrix-vector products
• On the relation between algebraic stability and B-convergence for Runge- Kutta methods
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Contractivity of Runge-Kutta methods
• Positivity of Runge-Kutta and diagonally split Runge-Kutta methods
• The positivity of low-order explicit Runge-Kutta schemes applied in splitting methods.
• Convergence and nonnegativity of numerical methods for an integrodifferential equation describing batch grinding
• Discrete maximum principle for linear parabolic problems solved on hybrid meshes
• A positive splitting method for mixed hyperbolic-parabolic systems
• Modified mass matrices and positivity preservation for hyperbolic and parabolic PDEs
• Conservation de la positivité lors de la discrétisation des problèmes d'évolution paraboliques
• Generalized trapezoidal formulas for parabolic equations
• Stepsize Restrictions for the Total-Variation-Diminishing Property in General Runge--Kutta Methods