TITLE:
Approximate Solution of the Singular-Perturbation Problem on Chebyshev-Gauss Grid
AUTHORS:
Mustafa GÜLSU, Yalçn ÖZTÜRK
KEYWORDS:
Singular Perturbation Problems, Two-Point Boundary Value Problems, The Shifted Chebyshev Polynomials, Approximation Method, Matrix Method
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.1 No.4,
December
9,
2011
ABSTRACT: Matrix methods, now-a-days, are playing an important role in solving the real life problems governed by ODEs and/or by PDEs. Many differential models of sciences and engineers for which the existing methodologies do not give reliable results, these methods are solving them competitively. In this work, a matrix methods is presented for approximate solution of the second-order singularly-perturbed delay differential equations. The main characteristic of this technique is that it reduces these problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The error analysis and convergence for the proposed method is introduced. Finally some experiments and their numerical solutions are given.