scholarly journals Numerical solution of delay differential equation using two-derivative Runge-Kutta type method with Newton interpolation

2021 ◽  
Author(s):  
N. Senu ◽  
K.C. Lee ◽  
A. Ahmadian ◽  
S.N.I. Ibrahim
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Delay Differential Equation ◽  
Newton Interpolation ◽  
Type Method ◽  
Runge Kutta ◽  
Delay Differential

scholarly journals Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Haiyan Yuan ◽  
Jingjun Zhao ◽  
Yang Xu
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Stability And Convergence ◽  
Runge Kutta ◽  
Lagrangian Interpolation ◽  
The Stability ◽  
Delay Differential

This paper is devoted to the stability and convergence analysis of the additive Runge-Kutta methods with the Lagrangian interpolation (ARKLMs) for the numerical solution of a delay differential equation with many delays. GDN stability and D-Convergence are introduced and proved. It is shown that strongly algebraically stability gives D-Convergence DA, DAS, and ASI stability give GDN stability. Some examples are given in the end of this paper which confirms our results.

scholarly journals Different Approaches to the Modelling of COVID-19

2021 ◽  
Vol 22 (4) ◽  
pp. 515-531
Author(s):  
J. F. C. A. Meyer ◽  
M. Lima ◽  
C. C. Espitia ◽  
F. Longo ◽  
B. Laiate ◽  
...  
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Mathematical Modelling ◽  
Delay Differential Equation ◽  
Real World ◽  
Real World Data ◽  
Type Method ◽  
World Data ◽  
Delay Differential

In this paper some innovative aspects of the mathematical modelling of classic epidemiology problems for the study of models related to the COVID-19 pandemic dynamics are presented. In addition, they are compared to real-world data using numerical methods in order to approximate the solutions. One of these models includes a non-transmitting compartment and another one, a delay-differential equation in the SIR-type method. Finally, a comparative discussion of the results is also presented. 

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