Convergence analysis of sectional methods for solving breakage population balance equations-I: the fixed pivot technique |
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Authors: | Jitendra Kumar Gerald Warnecke |
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Institution: | 1.Institute for Analysis and Numerics,Otto-von-Guericke University Magdeburg,Magdeburg,Germany |
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Abstract: | In this work we study the convergence of the fixed pivot techniques (Kumar and Ramkrishna Chem. Eng. Sci. 51, 1311–1332, 1996) 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. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 65R20 |
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