Fitted mesh B-spline collocation method for solving self-adjoint singularly perturbed boundary value problems

Abstract

In this paper we develop B-spline collocation method for solving a class of self-adjoint singularly perturbed equations given by (0.1) −ϵ(a(x)y ′) ′+b(x)y(x)=g(x), a(x)⩾a ∗>0, a ′(x)⩾0, b(x)⩾b ∗>0, y(0)=α, y(1)=β. We use the fitted mesh technique to generate piecewise uniform mesh, and use B-spline method which leads to a tridiagonal linear system. The convergence analysis is given and the method is shown to have uniform convergence of second order. Numerical illustrations are given in the end to demonstrate the efficiency of our method.