Adaptive time-stepping for aggregation-shattering kinetics

TL;DR

This paper investigates adaptive time-stepping methods, particularly explicit Runge-Kutta schemes, to efficiently simulate aggregation-shattering kinetics, reducing computational cost while maintaining accuracy in complex nonlinear systems.

Contribution

It evaluates the performance of three explicit Runge-Kutta methods for aggregation-shattering kinetics, demonstrating improved efficiency in equilibrium and periodic solution simulations.

Findings

Adaptive methods reduce simulation time for equilibrium states.

Adaptive criteria improve stability and speed in periodic solutions.

Significant computational savings achieved without loss of accuracy.

Abstract

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.