calculation methods for reaction schemes
Calculation methods for ReactionScheme objects. The only quantities required in addition to the reaction scheme itself are the timestep (ms) and total runtime (ms). The RSpool elements of the reaction scheme contain their own initial concentrations.
The evolution of the concentrations of the various pools is computed by a fully implicit scheme using Newton's method to solve iteratively for successive timesteps. The difference scheme is unconditionally stable but the Newton's method iterations may not always converge. Reducing the timestep should always improve convergence. The difference scheme is exactly conservative so no material is gained or lost as long as the integration converges.
Discretization errors from the one-sided time differencing can be assessed by varying the timestep. Like most of the calculations implemented in Catacomb this scheme is chosen to be quick and robust for relatively large timesteps, tending to the exact solution for small steps.