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A numerical integration method is developed for solving more general singular perturbation problems. Firstly, we discuss the problems with mixed boundary conditions and a left end boundary layer. Secondly, we discuss the singular-singular perturbation problems. Finally, we discuss the problems with mixed boundary conditions and a right end layer. Numerical experiments with the method for several model linear and non-linear examples with left end boundary layer or right end boundary layer are presented and compared with exact solutions.