Simple Procedure for the Designation of Haar Wavelet Matrices for Differential Equations
Chang Phang, Piau Phang · 2008
Abstract — Wavelet transforms or wavelet analysis is a recently developed mathematical tool for many problems. Wavelets also can be applied in numerical analysis. In this paper, we apply Haar wavelet methods to solve ordinary differential equations with initial condition known. To avoid the tedious calculations and to promote the study of wavelets to beginners, we proposed a simple way to perform the calculations for the matrix representation. Three numerical examples are shown which including first, second, higher order differential equations with constant and variable coefficients. The results show that the proposed way are quite reasonable when compare to exact solution. Index Terms — Haar wavelet methods, matrix representation, ordinary differential equations, computer algebra system I.