Wavelet Based Numerical Scheme for Differential Equations

Wavelets have become a powerful tool for having applications in almost all the areas of engineering and science such as image coding, edge extraction, weather forecasting, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients. Fascinated by the ability of wavelets, an efficient numerical scheme for solving differential equations is presented in this paper. The local property of Haar wavelets is fully applied to shorten the calculation process in the task. Some illustrative examples included to observe the performance of the scheme.