Forward Euler for a finite sectional balance with a positivity CFL

Input a valid grid state $(n,L)$ with $n_i\ge 0$, a step $h>0$, and the finite sectional event rates of Finite sectional coagulation-fragmentation balance with reported overflow. The total per-particle loss rate is

${\mathrm{\Lambda }}_i(n)={\sum }_j{K}_{ij}{n}_j+{\beta }_i\mathrm{.}$

First validate the grid, state, rates, and daughter measures against the input conditions of Finite sectional coagulation-fragmentation balance with reported overflow, and require $h>0$; if any condition fails, return invalid-input without updating. For admissible inputs use exact arithmetic to evaluate the finite event sums defining $F$ and ${\mathrm{\Lambda }}_i$. If $h{\mathrm{\Lambda }}_i(n)>1$ for any coordinate, return cfl-failure without updating. Otherwise return success together with $(n^{+},L^{+})=(n,L)+hF(n,L)$. Exact-arithmetic positivity and conservation are stated separately in The sectional forward-Euler step is positive and conserves augmented mass ↗.