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

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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.

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Authors and Affiliations

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

    Wen-zhi Zhang  (张文志) & Pei-yan Huang  (黄培彦)

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  1. Wen-zhi Zhang  (张文志)
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  2. Pei-yan Huang  (黄培彦)
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Project supported by the National Natural Science Foundation of China (Key Program)(Nos. 11132004 and 51078145)

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Zhang, Wz., Huang, Py. Coupling of high order multiplication perturbation method and reduction method for variable coefficient singular perturbation problems. Appl. Math. Mech.-Engl. Ed. 35, 97–104 (2014). https://doi.org/10.1007/s10483-014-1775-x

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  • DOI: https://doi.org/10.1007/s10483-014-1775-x

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Chinese Library Classification

2010 Mathematics Subject Classification

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