Asymptotic Solution for Model with Small Parameter

被引：0

作者：

Cai, Xin ^{[1
]}

机构：

[1] Zhejiang Univ Sci & Technol, Sch Sci, Hangzhou 310023, Zhejiang, Peoples R China

来源：

2009 SECOND INTERNATIONAL SYMPOSIUM ON KNOWLEDGE ACQUISITION AND MODELING: KAM 2009, VOL 1 | 2009年

关键词：

small parameter; asymptotic solution; ordinary differential equation; Gronwall inequality;

D O I：

10.1109/KAM.2009.76

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Model with small parameter is considered. Such problem undergo rapid changes within the boundary layer since the presence of the small parameter. Firstly, the analytical result of the problem is studied. The bound of the analytical solution is presented by Gronwall inequality. Secondly, the analytical solution is decomposed into the computational component and the small component. It is proved to be uniformly bound with respect to the small parameter in order one for the small component. Finally, numerical experiment is given to support the theoretical result.

引用

页码：168 / 171

页数：4

共 50 条

[1] Combining Asymptotic Solution and Numerical Solution for Differential Equation with Small Parameter
Cai, Xin
2009 SECOND INTERNATIONAL SYMPOSIUM ON KNOWLEDGE ACQUISITION AND MODELING: KAM 2009, VOL 2, 2009, : 201 - 204
[2] Asymptotic behavior of the solution to an equation with a small parameter
E. F. Lelikova
Doklady Mathematics, 2009, 80 : 852 - 855
[3] Asymptotic behavior of the solution to an equation with a small parameter
Lelikova, E. F.
DOKLADY MATHEMATICS, 2009, 80 (03) : 852 - 855
[4] Asymptotic behavior of the solution to a differential equation with a small parameter when the stability lines of the limit solution intersect
S. F. Dolbeeva
A. M. Il’in
Doklady Mathematics, 2006, 73 : 388 - 390
[5] Asymptotic Solution of the Cauchy Problem for a First-Order Differential Equation with a Small Parameter in a Banach Space
V. I. Uskov
Mathematical Notes, 2021, 110 : 145 - 151
[6] Asymptotic Solution of the Cauchy Problem for a First-Order Differential Equation with a Small Parameter in a Banach Space
Uskov, V. I.
MATHEMATICAL NOTES, 2021, 110 (1-2) : 145 - 151
[7] Asymptotic Solution of Optimal Control Problems with a Small Parameter and Intermediate Points in Performance Index
Kurina, Galina A.
Smirnova, Elena V.
COMPLEX ANALYSIS AND DYNAMICAL SYSTEMS IV, PT 1: FUNCTION THEORY AND OPTIMIZATION, 2011, 553 : 173 - 199
[8] The asymptotic behaviour of the solution to a system of differential equations with a small parameter and singular initial point
Il'in, A. M.
Leonychev, Yu. A.
Khachay, O. Yu.
SBORNIK MATHEMATICS, 2010, 201 (1-2) : 79 - 101
[9] Asymptotic behavior of the solution to the cauchy problem for a Hamilton-Jacoby equation depending on a small parameter
A. R. Danilin
Doklady Mathematics, 2006, 73 : 214 - 216
[10] Asymptotic behavior of the solution to the Cauchy problem for a Hamilton-Jacoby equation depending on a small parameter
Danilin, A. R.
DOKLADY MATHEMATICS, 2006, 73 (02) : 214 - 216

← 1 2 3 4 5 →