Some stability results for explicit Runge-Kutta methods

DOI10.1007/BF01933217zbMath0718.65061OpenAlexW2514988156MaRDI QIDQ2639609

Kristian Seip, Brynjulf Owren

Publication date: 1990

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01933217

zbMATH Keywords

upper boundstability regionpositive functionsstability polynomialexplicit m-stage Runge-Kutta methodslargest disk

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items

Some stability results for explicit Runge-Kutta methods, Essentially optimal explicit Runge-Kutta methods with application to hyperbolic-parabolic equations, Many-stage optimal stabilized Runge-Kutta methods for hyperbolic partial differential equations, A uniqueness result related to the stability of explicit Runge-Kutta methods, New stability results for explicit Runge-Kutta methods

Cites Work

• Stability of explicit time discretizations for solving initial value problems
• Absolute monotonicity of polynomials occuring in the numerical solution of initial value problems
• Some stability results for explicit Runge-Kutta methods
• Largest disk of stability of explicit Runge-Kutta methods
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