Recent literature reports two sectional techniques, the finite volume method
[Das et al., 2020, SIAM J. Sci. Comput., 42(6): B1570-B1598] and the fixed
pivot technique [Kushwah et al., 2023, Commun. Nonlinear Sci. Numer. Simul.,
121(37): 107244] to solve one-dimensional collision-induced nonlinear particle
breakage equation. It is observed that both the methods become inconsistent
over random grids. Therefore, we propose a new birth modification strategy,
where the newly born particles are proportionately allocated in three adjacent
cells, depending upon the average volume in each cell. This modification
technique improves the numerical model by making it consistent over random
grids. A detailed convergence and error analysis for this new scheme is studied
over different possible choices of grids such as uniform, nonuniform,
locally-uniform, random and oscillatory grids. En outre, we have also
identified the conditions upon kernels for which the convergence rate increases
significantly and the scheme achieves second order of convergence over uniform,
nonuniform and locally-uniform grids. The enhanced order of accuracy will
enable the new model to be easily coupled with CFD-modules. Another significant
advancement in the literature is done by extending the discrete model for
two-dimensional equation over rectangular grids.

Cet article explore les excursions dans le temps et leurs implications.

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