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

Abstract

We consider a difference scheme based on cubic spline in tension for second-order singularly perturbed boundary-value problem of the form

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.

Keywords:

• Cubic spline in tension
• Boundary layers
• Monotone matrix
• Irreducible matrix