An operational Haar wavelet collocation method for solving singularly perturbed boundary-value problems

Abstract

The basic aim of this study is to introduce and describe a numerical scheme for the approximate solutions of the one-dimensional singularly perturbed boundary-value problems. The method is based on Haar wavelets and its main characteristic is that, it converts the given problem into a system of algebraic equations that can be solved easily with any of the usual methods. Another distinguishing feature of the this method is that unlike several other numerical methods, it does not require conversion of a boundary value problem into initial-value problem and hence eliminates the possibility of unstable solutions. To show the accuracy and the efficiency of the method, several benchmark problems are implemented and the comparisons are given with other methods existing in the recent literature. The results of numerical tests confirm that the Haar wavelet collocation method is superior to other existing ones and is highly accurate.