A collocation approximation of singularly perturbed second order ordinary differential equation

Abstract

This paper concerns the numerical solutions of two-point singularly perturbed boundary value problems for second order ordinary differential equations. For the linear problem, Canonical polynomials are constructed as new basis for collocation solution in the smooth region which is superposed with an exponential function in the boundary layer region. Numerical examples are given which show that the exponential fitting leads to a numerical asymptotic procedure. Extension to nonlinear problems is demonstrated by an example.

Keywords:

• Canonical polynomials
• exponential fitting
• collocation approximation
• singularly perturbed B.V. problem

^† The author acknowledges the Senate Research Grant of the University of Ilorin.

^∗ Author to communicate concerning this paper.

^† The author acknowledges the Senate Research Grant of the University of Ilorin.

^∗ Author to communicate concerning this paper.

Notes

^† The author acknowledges the Senate Research Grant of the University of Ilorin.

^∗ Author to communicate concerning this paper.