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

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.