Implementation of Auto-Correlation Functions of Compactly Supported Wavelets to Population Balance Differential Equation

In this article, we discuss on the application of auto-correlation functions of Daubechies wavelets to solve the population balance differential equation. For this purpose, we first ap- proximat the derivative of auto-correlation functions, then by using the interpolation property of this functions, we approximate the solution. Since approximation matrix derivative of these functions is ill conditioned matrix, for areas near the boundary, Lagrange interpolation is used.