Haar Wavelet Matrices Designation in Numerical Solution of Ordinary 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 or boundary 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. The procedure applied in this paper is taking the Haar Series for the highest order of differential and integrate the series. Four 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.