Stability of Runge-Kutta methods for linear delay differential equations

2000 ◽  
Vol 87 (2) ◽  
pp. 355-371 ◽  
Author(s):  
S. Maset
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Linear Delay ◽  
Runge Kutta ◽  
Delay Differential

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 An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Süleyman Cengizci
Keyword(s):  
Differential Equations ◽  
Hybrid Method ◽  
Delay Differential Equations ◽  
Numerical Procedure ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Singularly Perturbed ◽  
Convection Term ◽  
Linear Delay ◽  
Delay Differential

In this work, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called Successive Complementary Expansion Method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, we employ a numerical procedure to solve the resulting equations that come from SCEM procedure. In order to show efficiency of this numerical-asymptotic hybrid method, we compare the results with exact solutions if possible; if not we compare with the results that are obtained by other reported methods.

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