Global convergence method for singularly perturbed boundary value problems

Abstract

We give uniformly convergent splines difference scheme for singularly perturbed boundary value problems (1) - εu″ + p(x)u′ + q(x)u = f(x), u(a) = α0, u(b) = α1, by using splines fitted with delta sequence due to the very stiff nature of the problem under consideration. We prove the O(min(h2, ε2)) order of uniform convergence with respect to small parameter ε at nodes on uniform mesh and O(min(h, ε)) order of uniform global convergence with respect to the approximate solution given by S(x) = ∑i=1N SΔi (x) H(xi - x) where H is the Heaviside function, which is the approximation for the closed form of the exact solution. © 2004 Elsevier B.V. All rights reserved.