Solving singularly perturbed boundary-value problems by spline in tension

Abstract

The difference scheme via spline in tension for the problem: - ε{lunate}y″ + p(x)y = f(x), p(x)\s>0, y(0) = α0, y(1) = α1, is derived. The error of the form O(h min(h, √ε{lunate}) is obtained. When p(x) = p = const., the corresponding spline in tension achieves the second order of the global uniform convergence. © 1988.