Non-polynomial spline solution of singularly perturbed boundary-value problems

A generalized scheme based on quartic non-polynomial spline functions is proposed. This scheme is designed for numerical solution of singularly perturbed two-point boundary-value problems arising in the study of science and engineering. The scheme leads to a five-diagonal linear system of equations. Convergence analysis of the method is briefly discussed. Two numerical examples each of constant and variable coefficients are given to show practical usefulness of the method.