On the asymptotic stability properties of Runge-Kutta methods for delay differential equations

1997 ◽  
Vol 77 (4) ◽  
pp. 467-485 ◽  
Author(s):  
Nicola Guglielmi
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Stability Properties ◽  
Runge Kutta ◽  
Delay Differential

scholarly journals Stepsize Restrictions for Nonlinear Stability Properties of Neutral Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Wei Gu ◽  
Ming Wang ◽  
Dongfang Li
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Nonlinear Stability ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Stability Properties ◽  
Neutral Delay Differential Equations ◽  
Runge Kutta ◽  
Delay Differential ◽  
The Relationship

The present paper is concerned with the relationship between stepsize restriction and nonlinear stability of Runge-Kutta methods for delay differential equations. We obtain a special stepsize condition guaranteeing global and asymptotical stability properties of numerical methods. Some confirmations of the conditions on Runge-Kutta methods are illustrated at last.

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