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In this paper, we introduce the convergence analysis of the fixed pivottechnique given by S.Kumar and Ramkrishna \cite{Kumar:1996-1} for the nonlinearaggregation population balance equations which are of substantial interest inmany areas of science: colloid chemistry, aerosol physics, astrophysics,polymer science, oil recovery dynamics, and mathematical biology. Inparticular, we investigate the convergence for five different types of uniformand non-uniform meshes which turns out that the fixed pivot technique is secondorder convergent on a uniform and non-uniform smooth meshes. Moreover, ityields first order convergence on a locally uniform mesh. Finally, the analysisexhibits that the method does not converge on an oscillatory and non-uniformrandom meshes. Mathematical results of the convergence analysis are alsodemonstrated numerically.

Convergence analysis of sectional methods for solving aggregation population balance equations: The fixed pivot technique