A review on singularly perturbed differential equations with turning points and interior layers

被引：54

作者：

Sharma, Kapil K. ^{[1
]}

Rai, Pratima ^{[2
]}

Patidar, Kailash C. ^{[3
]}

机构：

[1] SAU, Dept Math, New Delhi 110021, India

[2] Amity Univ, Amity Inst Appl Sci, Dept Math, Noida 201303, Uttar Pradesh, India

[3] Univ Western Cape, Dept Math & Appl Math, ZA-7535 Bellville, South Africa

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 22期

基金：

新加坡国家研究基金会;

关键词：

Singular perturbation; Turning points; Discontinuous data; Ordinary differential equations; Partial differential equations; Asymptotic analysis; Numerical analysis; BOUNDARY-VALUE-PROBLEMS; CONVECTION-DIFFUSION PROBLEMS; ASYMPTOTIC-NUMERICAL-METHOD; MESH SELECTION STRATEGY; FINITE-ELEMENT-METHOD; UNIFORM SIMPLIFICATION; SUFFICIENT CONDITIONS; INTERNAL LAYERS; COUPLED SYSTEM; RESONANCE;

D O I：

10.1016/j.amc.2013.04.049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Singular perturbation problems with turning points arise as mathematical models for various physical phenomena. The problem with interior turning point represent one-dimensional version of stationary convection-diffusion problems with a dominant convective term and a speed field that changes its sign in the catch basin. Boundary turning point problems, on the other hand, arise in geophysics and in modeling thermal boundary layers in laminar flow. In this paper, we review some existing literature on asymptotic and numerical analysis of singularly perturbed turning point and interior layer problems. The purpose is to find out what problems are treated and what numerical/asymptotic methods are employed, with an eye towards the goal of developing general methods to solve such problems. Since major work in this area started after 1970 so this paper limits its coverage to the work done by numerous researchers between 1970 and 2011. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：10575 / 10609

页数：35

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