  In this paper, we introduce the convergence analysis of the fixed pivot
technique given by S.Kumar and Ramkrishna \cite{Kumar:1996-1} for the nonlinear
aggregation population balance equations which are of substantial interest in
many areas of science: colloid chemistry, aerosol physics, astrophysics,
polymer science, oil recovery dynamics, and mathematical biology. In
particular, we investigate the convergence for five different types of uniform
and non-uniform meshes which turns out that the fixed pivot technique is second
order convergent on a uniform and non-uniform smooth meshes. Moreover, it
yields first order convergence on a locally uniform mesh. Finally, the analysis
exhibits that the method does not converge on an oscillatory and non-uniform
random meshes. Mathematical results of the convergence analysis are also
demonstrated numerically.
