Wavelet Transform and Wavelet Based Numerical Methods: an Introduction

Wavelet transformation is a new development in the area of applied mathematics. Wavelets are mathematical tools that cut data or functions or operators into different frequency components, and then study each component with a resolution matching to its scale. In this article, we have made a brief discussion on historical development of wavelets, basic definitions, formulations of wavelets and different numerical meth- ods based on Haar and Daubechies wavelets for the numerical solution of differential equations, integral and integro-differential equations.

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