On the stability of adaptations of Runge-Kutta methods to systems of delay differential equations

1996 ◽  
Vol 22 (1-3) ◽  
pp. 237-250 ◽  
Author(s):  
K.J. in 't Hout
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Runge Kutta ◽  
The Stability ◽  
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.

Stability Aspects Of Explicit Runge-Kutta Method For Delay Differential Equations

2012 ◽  
Author(s):  
Fudziah Ismail ◽  
San Lwin Aung ◽  
Mohamed Suleiman
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Linear Delay ◽  
Different Types ◽  
Regions Of Stability ◽  
Runge Kutta ◽  
The Stability ◽  
Delay Differential

Persamaan pembezaan lengah linear (PPL) diselesaikan dengan kaedah Runge–Kutta menggunakan interpolasi yang berbeza bagi penghampiran sebutan lengahnya. Polinomial kestabilannya diterbitkan dan rantau kestabilannya dipersembahkan. Kata kunci: Runge-Kutta, persamaan pembezaan lengah, kestabilan, interpolasi The linear delay differential equations (DDEs) are solved by Runge–Kutta method using different types of interpolation to approximate the delay terms. The stability polynomials are derived and the respective regions of stability are presented. Key words: Runge-Kutta, delay differential equations, stability, interpolation

scholarly journals Directly Solving Special Second Order Delay Differential Equations Using Runge-Kutta-Nyström Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
M. Mechee ◽  
F. Ismail ◽  
N. Senu ◽  
Z. Siri
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Computational Time ◽  
Test Problems ◽  
Numerical Comparison ◽  
Standard Set ◽  
Runge Kutta ◽  
The Stability ◽  
Delay Differential

Runge-Kutta-Nyström (RKN) method is adapted for solving the special second order delay differential equations (DDEs). The stability polynomial is obtained when this method is used for solving linear second order delay differential equation. A standard set of test problems is solved using the method together with a cubic interpolation for evaluating the delay terms. The same set of problems is reduced to a system of first order delay differential equations and then solved using the existing Runge-Kutta (RK) method. Numerical results show that the RKN method is more efficient in terms of accuracy and computational time when compared to RK method. The methods are applied to a well-known problem involving delay differential equations, that is, the Mathieu problem. The numerical comparison shows that both methods are in a good agreement.

scholarly journals Stability of delay differential equations in the sense of Ulam on unbounded intervals

2019 ◽  
Vol 9 (2) ◽  
pp. 125-131 ◽  
Author(s):  
Süleyman Öğrekçi
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Stability Problem ◽  
The Stability ◽  
Delay Differential ◽  
Unbounded Intervals

In this paper, we consider the stability problem of delay differential equations in the sense of Hyers-Ulam-Rassias. Recently this problem has been solved for bounded intervals, our result extends and improve the literature by obtaining stability in unbounded intervals. An illustrative example is also given to compare these results and visualize the improvement.

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