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Coupling of high order multiplication perturbation method and reduction method for variable coefficient singular perturbation problems

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

Received date: 2012-12-12

  Revised date: 2013-04-09

  Online published: 2013-12-27

Abstract

Based on the precise integration method (PIM), a coupling technique of the high order multiplication perturbation method (HOMPM) and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value problems (TPBVPs) with one boundary layer. First, the inhomogeneous ordinary differential equations (ODEs) are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer matrix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.

Cite this article

ZHANG Wen-Zhi;HUANG Pei-Yan . Coupling of high order multiplication perturbation method and reduction method for variable coefficient singular perturbation problems[J]. Applied Mathematics and Mechanics, 2014 , 35(1) : 97 -104 . DOI: 10.1007/s10483-014-1775-x

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