Convergence analysis of sectional methods for solving breakage population balance equations-I: the fixed pivot technique

In this work we study the convergence of the fixed pivot techniques (Kumar and Ramkrishna, 1996, Chem. Eng. Sci., 51, 1311-1332) for breakage problems. In particular, the convergence is investigated on four different types of uniform and non-uniform meshes. It is shown that the fixed pivot technique is second order convergent on a uniform and non-uniform smooth meshes. Furthermore, it gives first order convergence on a locally uniform mesh. Finally the analysis shows that the method does not converge on a non-uniform random mesh. The mathematical results of convergence analysis are also validated numerically.