High order multiplication perturbation method for singular perturbation problems

YAN Bo; DU Juan; HU Ning; SEKINE Hideki; ZHANG Wen-Zhi; HUANG Pei-Yan

doi:10.1007/s10483-013-1753-x

Applied Mathematics and Mechanics >

2013 , Vol. 34 >Issue 11: 1383 - 1392

DOI: https://doi.org/10.1007/s10483-013-1753-x

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High order multiplication perturbation method for singular perturbation problems

YAN Bo ,
DU Juan ,
HU Ning ,
SEKINE Hideki ,
ZHANG Wen-Zhi ,
HUANG Pei-Yan

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School of Civil and Transportation Engineering, South China University of Technology, Guangzhou 510641, P. R. China

Received date: 2012-11-22

Revised date: 2013-04-09

Online published: 2013-11-01

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Abstract

This paper presents a high order multiplication perturbation method for singularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary differential equations (ODEs) are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.

Key words： finite element method; domain decomposition; boundary element method; finite element-boundary element coupling; singular perturbation problem (SPP); high order multiplication perturbation method; two-point boundary value problem; boundary layer

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YAN Bo , DU Juan , HU Ning , SEKINE Hideki , ZHANG Wen-Zhi , HUANG Pei-Yan . High order multiplication perturbation method for singular perturbation problems[J]. Applied Mathematics and Mechanics, 2013 , 34(11) : 1383 -1392 . DOI: 10.1007/s10483-013-1753-x

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