A Note on Unconditional Maximum Norm Contractivity of Diagonally Split Runge–Kutta Methods

DOI10.1137/0733055zbMath0855.65095OpenAlexW1970698703MaRDI QIDQ4887037

Karel J. in 't Hout

Publication date: 23 July 1996

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0733055

zbMATH Keywords

nonstiff problemswaveform relaxationdiagonally split Runge-Kutta methodsunconditional contractivityorder barrierdissipative differential equations\(B\)-consistency

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items

Stability of linear multistep methods for nonlinear neutral delay differential equations in Banach space ⋮ On the convergence of waveform relaxation methods for stiff nonlinear ordinary differential equations ⋮ Contractivity of continuous Runge-Kutta methods for delay differential equations ⋮ Efficient inequality-preserving integrators for differential equations satisfying forward Euler conditions ⋮ A numerical study of diagonally split Runge-Kutta methods for PDEs with discontinuities ⋮ NUMERICAL AND ANALYTIC DISSIPATIVITY OF THE θ-METHOD FOR DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED VARIABLE LAG ⋮ On the one-leg methods for solving nonlinear neutral differential equations with variable delay ⋮ Asymptotic stability, contractivity and dissipativity of one-leg \(\theta \)-method for non-autonomous delay functional differential equations ⋮ A review of theoretical and numerical analysis for nonlinear stiff Volterra functional differential equations ⋮ Positivity of Runge-Kutta and diagonally split Runge-Kutta methods ⋮ Issues with positivity-preserving Patankar-type schemes