Abstract
An approximate method for the numerical solution of a class of singularly perturbed two point boundary value problems is presented. The given region is divided into inner and outer regions. The original second-order problem is replaced by an asymptotically equivalent first-order problem and solved as an initial value problem in the inner region. A terminal boundary condition is then obtained from the solution of the inner region problem. In turn, an outer region problem is obtained, by replacing the second-order differential equation by an approximate first-order differential equation with a small deviating argument, and solved efficiently by employing the trapezoidal formula coupled with a discrete invariant imbedding algorithm. The proposed method is iterative on the terminal point of the inner region problem. Several numerical examples have been solved to demonstrate the applicability of the method.
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