The Chebyshev Wavelet Method for Numerical Solutions of A Fractional Oscillator

Abstract

Wavelet transform or wavelet analysis has been recently developed as a mathematical tool for many problems. This paper is concerned with the wavelet numerical method for solving partial differential equations (PDE’s). The method is based on discrete wavelet transform, using Chebyshev Wavelet Method (CWM) which can be used for solving fractional differential equations. Interest in solving the problem using the Chebyshev wavelet basis is due to its simplicity and efficiency in numerical approximations. Four numerical examples were shown and the results demonstrated that the proposed way can be quite reasonable while compared with exact solutions.