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

An operational Haar wavelet collocation method for solving singularly perturbed boundary-value... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png SeMA Journal Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Sociedad Española de Matemática Aplicada
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
2254-3902
eISSN
2281-7875
D.O.I.
10.1007/s40324-016-0094-9
Publisher site
See Article on Publisher Site

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.

Journal

SeMA JournalSpringer Journals

Published: Oct 4, 2016

References

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