Equilibrium attractivity of Runge-Kutta methods (Q2713131)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Equilibrium attractivity of Runge-Kutta methods |
scientific article |
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Equilibrium attractivity of Runge-Kutta methods (English)
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26 July 2001
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stiff systems
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implicit Runge-Kutta methods
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equilibrium attractivity
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algebraic stability
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collocation methods
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The equillibrium attractivity of Runge-Kutta methods is investigated. Equilibrium attractivity meas that the norm of \(f\) (for ODE: \(y'=f(y)\)) never increases. This property is dual to algebraic stability. Sufficient algebraic conditions are produced and equilibrium attractivity is proved for high order algebraically stable Runge-Kutta Radau-IIA, Lobatto-IIIC collocation methods and for not algebraically stable Runge-Kutta Lobatto-IIIA collocation method. Some multipoint monotonicity conditions are discussed.
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