A Comparative Study on the Numerical Solution for Singularly Perturbed Volterra Integro-Differential Equations

2021 ◽  
Author(s):  
Abhilipsa Panda ◽  
Jugal Mohapatra ◽  
Narahari Raji Reddy
Keyword(s):  
Differential Equations ◽  
Comparative Study ◽  
Numerical Solution ◽  
Singularly Perturbed

The numerical solution of differential equations governing the reflexion of long radio waves from the ionosphere. IV

1961 ◽  
Vol 260 (1302) ◽  
pp. 393-408 ◽  
Keyword(s):  
Differential Equations ◽  
Comparative Study ◽  
Numerical Solution ◽  
Digital Computer ◽  
Long Waves ◽  
Sharp Change ◽  
Radio Waves ◽  
Night Time ◽  
Ionosphere Model ◽  
Essential Properties

The previous papers in this series have described methods by which the differential equations governing the reflexion of long waves from the ionosphere may be solved with the use of an automatic digital computer, and have dealt with the application of these methods to some idealized ionosphere models. In this paper these methods are used in a comparative study of models which have been proposed for the day-time ionosphere in summer. The model whose theoretical reflecting properties most nearly agree with the experimental observations is found, and suggestions are made as to how it should be changed. A summary is given of the essential properties which an acceptable day-time ionosphere model must possess. The transition from day-time to night-time conditions in the ionosphere is also discussed, and it is shown that the sharp change in the reflexion coefficients can be accounted for qualitatively by the disappearance of a D -layer which might be present during the day at low level in the ionosphere.

scholarly journals Numerical Solution of Systems of Singularly Perturbed Differential Equations

2009 ◽  
Vol 9 (2) ◽  
pp. 165-191 ◽  
Author(s):  
T. Linss ◽  
M. Stynes
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Numerical Solution ◽  
Diffusion Coefficients ◽  
Second Order ◽  
Singularly Perturbed ◽  
Second Order Differential Equations ◽  
Diffusion Parameters ◽  
Small Parameters

AbstractA survey is given of current research into the numerical solution of timeindependent systems of second-order differential equations whose diffusion coefficients are small parameters. Such problems are in general singularly perturbed. The equations in these systems may be coupled through their reaction and/or convection terms. Only numerical methods whose accuracy is guaranteed for all values of the diffusion parameters are considered here. Some new unifying results are also presented.

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