Adaptive time-stepping for the multicomponent Smoluchowski equation

Recieved: 04/26/2026

Accepted: 05/05/2026

Keywords: multicomponent Smoluchowski equation, adaptive time stepping, tensor train, Runge–Kutta methods, low-rank representation, coagulation

Available in the on-line version with: 15.09.2026

To cite this article

Zaks R.T., Matveev S.A., Smirnov A.P. Adaptive time-stepping for the multicomponent Smoluchowski equation. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2026. N 3, p.42-51 https://doi.org/10.55959/MSU/0137–0782–15–2026–50–3–42–51.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Zaks R.T. (Lomonosov Moscow State University (MSU))
()
Matveev S.A. (Lomonosov Moscow State University (MSU))
()
Smirnov A.P. (Lomonosov Moscow State University (MSU))

Abstract

This work considers the problem of numerical solution of the multicomponent Smoluchowski coagulation equation using a low-rank representation in the tensor train (TT) format. An adaptive time-stepping approach based on a second-order Runge–Kutta method with local error control is proposed and tested. Numerical experiments are carried out for ballistic and generalized Brownian kernels in the two-dimensional case. The use of adaptive time stepping significantly reduces computational time compared to constant step size maintaining low relative error. The advantages of adaptive time stepping are most pronounced in the numerical solution of the problem of finding a steady-state solution of the two-component coagulation equation with a particle source. The results demonstrate the efficiency of adaptive methods for the multicomponent coagulation problems in combination with tensor decompositions.