The stability of a class of Runge-Kutta methods for delay differential equations
KJ In't Hout - Applied numerical mathematics, 1992 - Elsevier
Applied numerical mathematics, 1992•Elsevier
This paper deals with the stability analysis of Runge-Kutta type methods for delay differential
equations. We focus on the subclass of collocation methods with abscissae in [0, 1), and we
prove that all of these methods violate an important stability condition related to the class of
testproblems U′(t)= λU (t)+ μU (t− τ) with λ, μ∈ C, Re λ<−∣ μ;∣ and τ> 0.
equations. We focus on the subclass of collocation methods with abscissae in [0, 1), and we
prove that all of these methods violate an important stability condition related to the class of
testproblems U′(t)= λU (t)+ μU (t− τ) with λ, μ∈ C, Re λ<−∣ μ;∣ and τ> 0.
This paper deals with the stability analysis of Runge-Kutta type methods for delay differential equations. We focus on the subclass of collocation methods with abscissae in [0, 1), and we prove that all of these methods violate an important stability condition related to the class of testproblems U′(t)= λU (t)+ μU (t− τ) with λ, μ∈ C, Re λ<−∣ μ;∣ and τ> 0.
Elsevier
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