Initial-value technique for self-adjoint singular perturbation boundary value problems

Abstract

We have developed an initial-value technique for self-adjoint singularly perturbed two-point boundary value problems. The original problem is reduced to its normal form, and the reduced problem is converted into first-order initial-value problems. These initial-value problems are solved by the cubic spline method. Numerical illustrations are given at the end to demonstrate the efficiency of our method. Graphs are also depicted in support of the results.