Solving singularly perturbed boundary-value problems by spline in tension

摘要

The difference scheme via spline in tension for the problem: − ϵy″ + 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) is obtained. When p(x) = p = const., the corresponding spline in tension achieves the second order of the global uniform convergence.