Wavelet Method
Snehashish Chakraverty, Nisha Rani Mahato, Perumandla Karunakar, Tharasi Dilleswar Rao · 2019
Wavelet method has been proven to be an efficient tool in analyzing dynamic systems and differential equations arising in other science and engineering problems. A wave-like oscillation having amplitude beginning at zero that monotonically increases and then decreases back to zero is referred to as wavelet. Wavelets also serve as a tool in analysis of transient, nonstationary, and time-variate phenomena. The broad classification of wavelet classes is considered as discrete, continuous, and multiresolution-based wavelets. This chapter considers a basic idea of Haar wavelet. Further, just to have an overview of how to handle ordinary differential equation using Haar wavelets, a preliminary procedure is demonstrated. In this regard, the chapter discusses Haar wavelet-based wavelet-collocation method for solving ordinary differential equation. In order to solve the differential equation, highest-order derivative is expressed in terms of linear combination of Haar wavelet functions.