出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：A new algorithm is proposed for solving large networks of stiff coupled differential equations in
various scientific applications. The algorithm replaces differencing of abundance variables with
evolution of discrete populations. It reproduces quantitatively the results of standard methods,
but with important advantages. (1) The algorithm is explicit, yet it decouples accuracy from stability
for stiff systems, permitting explicit integration with a timestep set by the former rather
than the latter, thereby avoiding implicit solves. (2) It exploits sparseness perfectly, computing
only those reaction links that the physical system traverses. (3) It scales linearly with the number
of couplings for large sparse networks, in contrast to the quadratic to cubic scaling of standard
methods. (4) Unlike Monte Carlo, for large physical particle number, execution time is independent
of the number of test particles, allowing even weaker populations to be tracked efficiently.
(5) The decoupling of stability from accuracy allows stable tuning of large networks to optimize
accuracy versus computational time. We propose that this new approach can be used to solve
large, stiff networks for many complex systems, such as the coupling of realistic networks to
multidimensional hydrodynamics, that tax the capability of standard methods.
