Solutions of population balance equations by double Legendre polynomial transformation

Abstract

Abstract First‐order partial differential equations of population balance are solved by employing the Legendre polynomials. The key of the method is that the dependent variable of the population density function is assumed to be expressed by a double series of Legendre polynomials with respect to time and space variables. The approach algorithm is that a series of ordinary differential equations are obtained by making the Legendre transformation with respect to the space coordinate. The series of time‐function ordinary differential equations are further transformed into algebraic equations of expansion coefficients with respect to time. The expansion coefficients of the Legendre polynomials are obtained by solving matrix equations which represent the series of algebraic equations. Illustrative examples are given, and the computational results are compared with those of other numerical values given in the literature. Satisfactory agreements are obtained.