An implicit scheme for singularly perturbed parabolic problem with retarded terms arising in computational neuroscience

2018 ◽  
Vol 34 (6) ◽  
pp. 1933-1952 ◽  
Author(s):  
Devendra Kumar
Keyword(s):  
Computational Neuroscience ◽  
Parabolic Problem ◽  
Implicit Scheme ◽  
Singularly Perturbed ◽  
Singularly Perturbed Parabolic Problem

scholarly journals Singularly perturbed parabolic problem with oscillating initial condition

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1323-1327
Author(s):  
Asan Omuraliev ◽  
Ella Abylaeva
Keyword(s):  
Boundary Layer ◽  
Parabolic Problem ◽  
Singularly Perturbed ◽  
Initial Condition ◽  
Parabolic Boundary ◽  
Layer Function ◽  
Angular Boundary ◽  
Singularly Perturbed Parabolic Problem ◽  
Boundary Layer Function ◽  
Regularized Asymptotics

The aim of this paper is to construct regularized asymptotics of the solution of a singularly perturbed parabolic problem with an oscillating initial condition. The presence of a rapidly oscillating function in the initial condition has led to the appearance of a boundary layer function in the solution, which has the rapidly oscillating character of the change. In addition, it is shown that the asymptotics of the solution contains exponential, parabolic boundary layer functions and their products describing the angular boundary layers. Continuing the ideas of works [1, 3] a complete regularized asymptotics of the solution of the problem is constructed.

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