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

• Published in: Acta mechanica Sinica Vol. 29; no. 2; pp. 233 - 240
• Main Authors: Zhang, Wen-Zhi, Huang, Pei-Yan
• Format: Journal Article
• Language: English
• Published: Heidelberg The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences 01.04.2013
• Subjects: Algebra; boundary; Boundary value problems; Classical and Continuum Physics; Computational Intelligence; Differential equations; Engineering; Engineering Fluid Dynamics; High; integration; Mathematical analysis; Mathematical models; method; multiple; order; perturbation; Perturbation methods; point; Precise; problem; Reduction; Research Paper; Segments; Singular; Theoretical and Applied Mechanics; two; value; Reduction method; Singular two point boundary value problem; Precise integration method; High order multiple perturbation method
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-013-0006-5

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.