Paper Info
Title
Asymptotic-Numerical Method for the Location and Dynamics of Internal Layers in Singular Perturbed Parabolic Problems.
Abstract
A singularly perturbed initial-boundary value problem for the parabolic reaction-diffusion-advection (RDA) equation is considered. Some effective asymptotic-numerical approach for the description of internal layers location and moving fronts dynamics is proposed. Asymptotic analysis allows to reduce the spatial dimension of the numerical problem and highlight a priori information to optimize numerical calculations and save computational resources. But for some classes of RDA problems, featuring the internal layers or moving fronts, the layers location or fronts speed could not be found explicitly and asymptotic algorithm needs to be supplemented by the appropriate numerical calculations. In this paper we show the main ideas of the asymptotic algorithm for this type of solutions and outline some problems which need to use numerical calculations on some steps of the asymptotic procedure. The main features of numerical algorithm are presented.
Year
DOI
Venue
2016
10.1007/978-3-319-57099-0_83
Lecture Notes in Computer Science
Keywords
Field
DocType
Singularly perturbed parabolic problems,Reaction-diffusion-advection equation,Internal layers,Moving fronts,Asymptotic methods
Control theory,Mathematical analysis,Numerical analysis,Mathematics,Parabola
Conference
Volume
ISSN
Citations 
10187
0302-9743
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Vladimir Volkov120.80
Dmitry Lukyanenko202.70
Nikolay Nefedov374.41