Abstract
In this paper, a collocation method based on Haar wavelets is proposed for the numerical solutions of singularly perturbed boundary value problems. The properties of the Haar wavelet expansions together with operational matrix of integration are utilized to convert the problems into systems of algebraic equations with unknown coefficients. To demonstrate the effectiveness and efficiency of the method various benchmark problems are implemented and the comparisons are given with other methods existing in the recent literature. The demonstrated results confirm that the proposed method is considerably efficient, accurate, simple, and computationally attractive.
Highlights
Perturbed problems (SPPs) arise in various branches of applied mathematics and physics such as fluid mechanics, quantum mechanics, elasticity, plasticity, semi-conductor device physics, ABOUT THE AUTHORSFirdous A
His research interests are focused on different wavelet methods for the numerical treatment of integral and differential equations
The objective of this research is to construct a simple collocation method based on Haar wavelets for the numerical solution of singularly perturbed reaction–diffusion problems of the type (1.1) which arise in mathematical modeling of different engineering applications
Summary
Perturbed problems (SPPs) arise in various branches of applied mathematics and physics such as fluid mechanics, quantum mechanics, elasticity, plasticity, semi-conductor device physics, ABOUT THE AUTHORSFirdous A. Shah is a senior assistant professor in the Department of Mathematics at the University of Kashmir, India. His primary research interests include basic theory of wavelets and their applications in differential and integral equations, Economics and Finance, and Computer Networking. He has authored/co-authored over 60 research papers in international journals of high repute. He has recently co-authored a book on wavelets entitled Wavelet Transforms and Their Applications, Springer, New York, 2015. His research interests are focused on different wavelet methods for the numerical treatment of integral and differential equations
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