Sequential splitting is used in the numerical treatment.
We also prove convergence rates for the sequential splitting applied to this problem.
Sequential splitting of the largest component of the network with the edge betweenness algorithm [27] led to the identification of six compartments (Fig. 2B), which were validated statistically (Table 1).
The first pathway of triglyceride degradation involves, first, the split of the triester into the glycerol head and the three fatty acid chains [ 12](see figure 6.2-1), then, the sequential split of an acetyl group from each fatty acid [ 12](see figure 6.1-9), and, finally, the degradation of both the glycerol and acetyl molecules via the Krebs cycle [ 12](see figures 3.1-1, 3.3-1, and 3.8-2).
Most computer programs are sequential, and splitting them up so that chunks of them can run in parallel causes all kinds of complications.
A two-step sequential operator splitting method is used to solve the coupled transport and biogeochemical reaction equations.
The reactive transport equations are solved using the Strang splitting method which is shown to be accurate for Monod and first- and second-order kinetic reactions, and two to four times more efficient than sequential iterative splitting.
Our numerical method for solving these equations is based on a total-velocity splitting, sequential formulation which leads to an implicit pressure equation and a semi-implicit mass conservation equation.
Considering reactive mass transport with reversible and irreversible reactions governed by a first-order rate law, we develop analytical solutions of the mass balance for the following operator-splitting schemes: standard sequential non-iterative (SNI), Strang-splitting SNI, standard sequential iterative (SI), extrapolating SI, and symmetric SI approaches.
To overcome this obstacle, we suggest a quite general combination of sequential Monte Carlo and multilevel splitting.
