Abstract
The object of this paper is to present a new approach based on the method of inner boundary condition for solving singular perturbation problems. The original problem is partitioned into inner and outer region differential equation systems. Asymptotic expansion is used to obtain the terminal boundary condition. Using an appropriate transformation, a new inner region problem is obtained and solved as a two point boundary value problem. The derivative boundary condition at the terminal point is then derived from the solution of the inner region problem. Using this condition, the outer region problem is efficiently solved by employing the classical finite difference scheme. The proposed method is iterative on the terminal point. Some numerical examples have been solved to demonstrate the efficiency of the method.
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