scholarly journals Nonlinear stability of general linear methods for neutral delay differential equations

2009 ◽  
Vol 224 (2) ◽  
pp. 592-601 ◽  
Author(s):  
Wan-Sheng Wang ◽  
Shou-Fu Li ◽  
Kai Su
Keyword(s):  
Differential Equations ◽  
Nonlinear Stability ◽  
Delay Differential Equations ◽  
General Linear Methods ◽  
General Linear ◽  
Neutral Delay ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

scholarly journals Nonlinear Stability and Convergence of Two-Step Runge-Kutta Methods for Neutral Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Haiyan Yuan ◽  
Cheng Song ◽  
Peichen Wang
Keyword(s):  
Differential Equations ◽  
Nonlinear Stability ◽  
Delay Differential Equations ◽  
Stability And Convergence ◽  
Neutral Delay ◽  
Neutral Delay Differential Equations ◽  
Restricted Type ◽  
Runge Kutta ◽  
The Stability ◽  
Delay Differential

This paper is devoted to the stability and convergence analysis of the two-step Runge-Kutta (TSRK) methods with the Lagrange interpolation of the numerical solution for nonlinear neutral delay differential equations. Nonlinear stability and D-convergence are introduced and proved. We discuss theGR(l)-stability,GAR(l)-stability, and the weakGAR(l)-stability on the basis of(k,l)-algebraically stable of the TSRK methods; we also discuss the D-convergence properties of TSRK methods with a restricted type of interpolation procedure.

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.

scholarly journals Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Neutral Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.

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