Delay-dependent stability of symmetric Runge–Kutta methods for second order delay differential equations with three parameters

2017 ◽  
Vol 117 ◽  
pp. 103-114
Author(s):  
Jingjun Zhao ◽  
Yan Fan ◽  
Yang Xu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Runge Kutta ◽  
Delay Differential ◽  
Delay Dependent ◽  
Delay Dependent Stability

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 Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 318
Author(s):  
Osama Moaaz ◽  
Amany Nabih ◽  
Hammad Alotaibi ◽  
Y. S. Hamed
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Mixed Type ◽  
Relevant Literature ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Neutral Differential Equations ◽  
Delay Differential ◽  
Oscillation Of Solutions

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included.

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