Convergence analysis of sectional methods for solving aggregation population balance equations: The fixed pivot technique |
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Authors: | Ankik Kumar Giri Erika Hausenblas |
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Institution: | 1. Institute for Applied Mathematics, Montan University Leoben, Franz Josef Straße 18, A-8700 Leoben, Austria;2. Institute for Analysis and Numerics, Otto-von-Guericke University Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany |
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Abstract: | In this paper, we introduce the convergence analysis of the fixed pivot technique given by S. Kumar and Ramkrishna (1996) 28] 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. |
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