Boundedness and strong stability of Runge-Kutta methods

DOI10.1090/S0025-5718-2010-02422-6zbMath1218.65068OpenAlexW2163489274MaRDI QIDQ3168726

Marc N. Spijker, Willem H. Hundsdorfer

Publication date: 19 April 2011

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2010-02422-6

zbMATH Keywords

monotonicitynumerical examplesordinary differential equationsinitial value problemsmethod of linesRunge-Kutta methodstotal-variation-boundedstability and boundedness of solutionstotal-variation-diminishing property

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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

Related Items (6)

Strong stability for Runge-Kutta schemes on a class of nonlinear problems ⋮ Exact optimal values of step-size coefficients for boundedness of linear multistep methods ⋮ Unconditionally strong stability preserving extensions of the TR-BDF2 method ⋮ Optimized strong stability preserving IMEX Runge-Kutta methods ⋮ Strong stability preserving properties of composition Runge-Kutta schemes ⋮ Stabilized Integrating Factor Runge--Kutta Method and Unconditional Preservation of Maximum Bound Principle

Uses Software

• RODAS

Cites Work

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