SPLINE INTERPOLATION METHOD OF SOLVING SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM USING POLYNOMIAL AND NONPOLYNOMIAL SPLINES WITH ERROR COMPARISON
Keywords:
Singularly Perturbation, Polynomial and Non-polynomial Splines and Maximum Absolute Error.Abstract
We consider two polynomial Spline methods to calculate the numerical solution as well as the
maximum absolute errors of a singularly perturbed two point boundary value problems. The
two methods are linear and nonlinear polynomial spline and nonlinear polynomial Spline tends
to give accurate, stable and consistent results compared with the linear polynomial spline. Also
interms of the formulation of the two methods, the nonlinear polynomial spline is in terms of
differential equation of order two. The goal is to find the maximum absolute errors between
the liner polynomial and nonlinear polynomial spline methods in relation to the exact solution.
The applications of these splines to singularly perturbed two point boundary value problem
resulted to linear algebraic system of equations which are then solved by Gaussian elimination
method to obtain the unknown constants arising from the spline used.
