Perturbed segmented domain collocation Tau-method for the numerical solution of Second Order Boundary Value problems

Abstract

This paper concerns the numerical solution of second order boundary value problems using a Perturbed segmented domain collocation-Tau method. The entire interval for which the problem is defined is partitioned into two segments and the solution technique is demonstrated on each of the segments. The Chebyshev polynomials shifted as the case may be, into a given interval are used as a basis for a collocation solution via the perturbed collocation method for each segment. For a given problem two different solutions are obtained, which are valid for different intervals within the domain. Numerical examples are given to illustrate the efficiency, accuracy and computational cost of the method. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 293-298