A parameter expansion method for two-point nonlinear singularly-perturbed boundary value problems

Abstract

This paper presents a parameter expansion method for two-point nonlinear singularly perturbed boundary value problem for second order ordinary differential equation. Newton's linearization scheme is used to linearize the nonlinear problems. In Okoro et al. [1] linear problems were treated. The numerical results obtained for some examples show that the parameter expansion becomes more accurate as the value of ε approaches zero when compared with the standard collocation method, at no extra computational effort. For favourable problems to exponential fitting reported in [2], the proposed method in this paper is less accurate. It is however more general in application than the exponential fitting.

Keywords:

• Parameter expansion
• Newton's linearization'
• exponential fitting
• collocation
• Chebyshev polynomial perturbation
• Stiffness