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2009-35

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

by Giri, A.K., Kumar, J., Warnecke, G..


Series: 2009-35, Preprints

MSC:
45J05 Integro-ordinary differential equations
65R20 Integral equations

Abstract:
In this paper, we introduce the convergence analysis of the fixed pivot technique given by S. Kumar and Ramkrishna [22] for the nonlinear aggregation population balance equations whiche 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 nonuniform 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. The mathematical results of the convergence analysis are also justified numerically.

Keywords:
Particles; Fixed pivot technique; Consistency; Convergence