A wavelet-Galerkin method for solving population balance equations

A new wavelet-Galerkin method is developed to solve the population balance equations which arise in the description of particle-size distribution of a continuous, mixed-suspension, mixed-product removal crystallizer with taking account of the effect of particle breakage. The class of Daubechies wavelets, which is both compactly supported and orthonormal, is adopted as the Galerkin bases. Some elegant results concerned with the exact evaluation of functions on wavelets and their derivatives and integrals are derived. These results along with the 2-scale relation which defines the wavelet bases make the Galerkin method feasible for the solution of population balance equations containing a scaled argument.