scholarly journals Design of a Novel Second-Order Prediction Differential Model Solved by Using Adams and Explicit Runge–Kutta Numerical Methods

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Zulqurnain Sabir ◽  
Juan L. G. Guirao ◽  
Tareq Saeed ◽  
Fevzi Erdoğan
Keyword(s):  
Numerical Methods ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Second Order ◽  
The Novel ◽  
Differential Model ◽  
Runge Kutta ◽  
Delay Differential ◽  
The Mind ◽  
Novel Model

In this study, a novel second-order prediction differential model is designed, and numerical solutions of this novel model are presented using the integrated strength of the Adams and explicit Runge–Kutta schemes. The idea of the present study comes to the mind to see the importance of delay differential equations. For verification of the novel designed model, four different examples of the designed model are numerically solved by applying the Adams and explicit Runge–Kutta schemes. These obtained numerical results have been compared with the exact solutions of each example that indicate the performance and exactness of the designed model. Moreover, the results of the designed model have been presented numerically and graphically.

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 Numerical Solution of Fuzzy Delay Differential Equations by Fifth Order Runge-Kutta Method

2021 ◽  
Vol 23 (11) ◽  
pp. 99-109
Author(s):  
T. Muthukumar ◽  
◽  
T. Jayakumar ◽  
D.Prasantha Bharathi ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Kutta Method ◽  
Numerical Examples ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Delay Differential ◽  
Fifth Order

In this paper, we develop the numerical solutions of certain type called Fuzzy Delay Differential Equations(FDE) by using fifth order Runge-Kutta method for fuzzy differential equations. This method based on the seikkala derivative and finally we discuss the numerical examples to illustrate the theory.

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 Design and Numerical Solutions of a Novel Third-Order Nonlinear Emden–Fowler Delay Differential Model

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Juan L.G. Guirao ◽  
Zulqurnain Sabir ◽  
Tareq Saeed
Keyword(s):  
Numerical Solutions ◽  
Standard Form ◽  
Numerical Results ◽  
Third Order ◽  
Multiple Points ◽  
Shape Factors ◽  
Differential Model ◽  
Delay Differential ◽  
Global And Local ◽  
Novel Model

In this study, the design of a novel model based on nonlinear third-order Emden–Fowler delay differential (EF-DD) equations is presented along with two types using the sense of delay differential and standard form of the second-order EF equation. The singularity at ξ = 0 at single or multiple points of each type of the designed EF-DD model are discussed. The detail of shape factors and delayed points is provided for both types of the designed third-order EF-DD model. For the verification and validation of the model, two numerical examples are presented of each case and numerical results have been performed using the artificial neural network along with the hybrid of global and local capabilities. The comparison of the obtained numerical results with the exact solutions shows the perfection and correctness of the designed third-order EF-DD model.

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.

scholarly journals New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1159
Author(s):  
Shyam Sundar Santra ◽  
Omar Bazighifan ◽  
Mihai Postolache
Keyword(s):  
Fluid Dynamics ◽  
Neural Networks ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Qualitative Behavior ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Delay Differential

In continuous applications in electrodynamics, neural networks, quantum mechanics, electromagnetism, and the field of time symmetric, fluid dynamics, neutral differential equations appear when modeling many problems and phenomena. Therefore, it is interesting to study the qualitative behavior of solutions of such equations. In this study, we obtained some new sufficient conditions for oscillations to the solutions of a second-order delay differential equations with sub-linear neutral terms. The results obtained improve and complement the relevant results in the literature. Finally, we show an example to validate the main results, and an open problem is included.

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