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Precise integration method for a class of singular two-point boundary value problems

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Abstract

In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems. Firstly, by employing the method of variable coefficient dimensional expanding, the non-homogeneous ordinary differential equations (ODEs) are transformed into homogeneous ODEs. Then the interval is divided evenly, and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method, and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment, which is worked out by the reduction method. Finally numerical examples are elaboratedd to validate the present method.

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Authors and Affiliations

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

    Wen-Zhi Zhang & Pei-Yan Huang

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  1. Wen-Zhi Zhang
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  2. Pei-Yan Huang
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Correspondence to Pei-Yan Huang.

Additional information

The project was supported by the National Natural Science Foundation of China (11132004 and 51078145) and the Natural Science Foundation of Guangdong Province (9251064101000016).

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Zhang, WZ., Huang, PY. Precise integration method for a class of singular two-point boundary value problems. Acta Mech Sin 29, 233–240 (2013). https://doi.org/10.1007/s10409-013-0006-5

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  • DOI: https://doi.org/10.1007/s10409-013-0006-5

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