A spline method for second-order singularly perturbed boundary-value problems

We consider a difference scheme based on cubic spline in compression for second-order singularly perturbed boundary value problem of the formεy″=p(x)y′+q(x)y+r(x), y(a)=α0, y(b)=α1.The method is shown to have second- and fourth-order convergence depending on the choice of parameters λ1 and λ2 involved in the method. The method is tested on an example and the results found to be in agreement with the theory.