We propose an experimental study of adaptive time-stepping methods for efficient modeling of the aggregation-fragmentation kinetics. Precise modeling of this phenomena usually requires utilization of the large systems of nonlinear ordinary differential equations and intensive computations. We concentrate on performance of three explicit Runge-Kutta time-integration methods and provide simulations for two types of problems: finding of equilibrium solutions and simulations for kinetics with periodic solutions. The first class of problems may be analyzed through the relaxation of the solution to the stationary state after large time. In this case, the adaptive time-stepping may help to reach it using big steps reducing cost of the calculations without loss of accuracy. In the second case, the problem becomes numerically unstable at certain points of the phase space and may require tiny steps making the simulations very time-consuming. Adaptive criteria allows to increase the steps for most of points and speedup simulations significantly.

翻译：本文提出了一种自适应时间步长方法的实验研究，用于高效模拟聚集-破碎动力学过程。该现象的精确建模通常需要求解大规模非线性常微分方程组并进行密集计算。我们重点研究了三种显式龙格-库塔时间积分方法的性能，并对两类问题进行了数值模拟：平衡解的求解与周期解动力学模拟。第一类问题可通过长时间后解向稳态的弛豫过程进行分析。在此情况下，自适应时间步长方法能够通过采用较大步长来降低计算成本，同时保持精度，从而高效达到稳态。第二类问题在相空间特定点处会出现数值不稳定性，可能需要极小的步长，导致模拟计算量巨大。自适应判据能够在多数相空间点采用较大步长，从而显著加速模拟过程。