A Comparative Study of Haar Wavelet-Based Numerical Solution and Exact Solution of Differential Equation

摘要

Wavelet is relatively new but an emerging theory in the field of mathematics and signal processing which is being used in different engineering and mathematical tasks. From many existing wavelets, the Haar wavelet is one of the popular in mathematics and engineering due to its simplicity and compact support. In my study, the Haar wavelet operational matrix method is used to solve 2^nd order ordinary differential equations as well as two-dimensional partial differential equations. Comparing to the conventional methods Haar wavelet method is easy to find the required integral to solve differential equations. By making the block pulse operational matrix and Haar wavelet matrix, Haar wavelet operational matrix can be formed. Using the Haar wavelet the differential equation can be decomposed in the Haar series, and the integral can be calculated to get the numerical solution. The numerical solution of the Haar wavelet-based method is compared to the exact solution, and it gives very little error.