Numerical solution of differential equations by using Haar wavelets

Abstract

This paper establishes a clear procedure for finite-length beam problem and convection-diffusion equation solution via Haar wavelet technique. An operational matrix of integration based on the Haar wavelet is established,and the procedure for applying the matrix to solve the differential equations is formulated. The fundamental idea of Haar wavelet method is to convert the differential equations into a group of algebra equations which involves a finite number of variables. Illustrative examples are given to demonstrate the fast and flexible of the method ,in the mean time,it is found that the trouble of Daubechies wavelets for solving the differential equations which need to calculate the correlation coefficients is avoided. The method can be used to deal with all the other differential and integral equations.