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A deterministic scheme for Smoluchowski's coagulation equation based on binary grid refinement

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Abstract

We present a deterministic scheme for the discrete Smoluchowski's coagulation equation based on a binary grid refinement. Starting from the binary grid Ω0={1,2,4,8,16,. . .}, we first introduce an appropriate grid refinement by adding at each level 2l grid points in every binary subsection of the grid Ωl. In a next step we derive an approximate equation for the dynamic behavior on each level Ωl based on a piecewise constant approximation of the right hand side of Smoluchowski's equation. Numerical results show that the computational effort can be drastically decreased compared to the corresponding complete integer grid. When considering unbounded kernels in Smoluchowski's equation we use an adaptive time step method to overcome numerical instabilities which may occur at the tails of the density function.

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Authors and Affiliations

  1. Department of Mathematics, University of Hamburg, Bundesstr. 55, D-20146, Hamburg, Germany

    Jens Struckmeier

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  1. Jens Struckmeier
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Correspondence to Jens Struckmeier.

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Communicated by C. Brezinski

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Struckmeier, J. A deterministic scheme for Smoluchowski's coagulation equation based on binary grid refinement. Numer Algor 40, 233–249 (2005). https://doi.org/10.1007/s11075-005-4186-3

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  • DOI: https://doi.org/10.1007/s11075-005-4186-3

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