scholarly journals Solving a novel designed second order nonlinear Lane–Emden delay differential model using the heuristic techniques

2021 ◽  
Vol 102 ◽  
pp. 107105
Author(s):  
Zulqurnain Sabir ◽  
Juan L.G. Guirao ◽  
Tareq Saeed
Keyword(s):  
Second Order ◽  
Differential Model ◽  
Heuristic Techniques ◽  
Delay Differential

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 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.

scholarly journals Pharmacokinetic modeling of Gadolinium nanoparticles (Gd-NPs) with the sojourn time in vasa vasorum for the contrast enhanced MRI

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Angkhana Prommarat ◽  
Farida Chamchod
Keyword(s):  
Sojourn Time ◽  
Vasa Vasorum ◽  
Peripheral Arteries ◽  
Resonance Imaging ◽  
Differential Model ◽  
Transfer Rates ◽  
Dynamical Behaviors ◽  
Contrast Enhanced ◽  
Delay Differential

AbstractDeposition of lipid in the artery wall called atherosclerosis is recognized as a major cause of cardiovascular disease that leads to death worldwide. A better understanding into factors that may influence the delivery of gadolinium nanoparticles (Gd-NPs) that enhances quality of magnetic resonance imaging in diagnosis may provide a vital key for atherosclerotic treatment. In this study, we propose a delay differential model for describing the dynamics of Gd-NPs in bloodstream, peripheral arteries, and vasa vasorum with two phenomena of Gd-NPs during a sojourn in vasa vasorum. We then investigate the dynamical behaviors of Gd-NPs and explore the effects of sojourn time and transfer rates of Gd-NPs on the concentration of Gd-NPs in vasa vasorum at the 12th hour after the administration of gadolinium chelates contrast media and also the maximum concentration of Gd-NPs in peripheral arteries and vasa vasorum. Our results suggest that the sojourn of Gd-NPs in vasa vasorum may lead to complex behaviors of Gd-NPs dynamics, and transfer rates of Gd-NPs may have a significant impact on the concentration of Gd-NPs.

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