A new approach to solve PBE (Population Balance Equations), FCMOM (Finite size domain Complete set of trial functions Method Of Moments), is presented. The solution of the PBE is sought, instead of the [0, infinity] range, in the finite interval between the minimum and maximum particle size; their evolution is tracked imposing moving boundaries conditions. After reformulating the PBE in the standard interval [-1, 1], the size distribution function is represented as a series expansion by a complete system of orthonormal functions. Moments evolution equations are developed from the PBE in the interval [-1, 1]. The FCMOM is implemented through an efficient algorithm and provides the solution of the PBE both in terms of the moments and in terms of the size distribution function. The FCMOM was validated with applications to particle growth (constant, linear, diffusion-controlled), simultaneous particle growth and nucleation, particle dissolution, particle aggregation (constant, sum, product, Brownian kernels) and simultaneous particle aggregation and growth. (C) 2008 Elsevier Ltd. All rights reserved.