Fast and accurate finite-difference method solving multicomponent Smoluchowski coagulation equation with source and sink terms

In this work we present novel numerical method solving multicomponent Smoluchowski coagulation equation. The new method is based on application of the fast algorithms of linear algebra and the fast arithmetics in tensor train format to acceleration of well-known highly accurate second order Runge-Kutta scheme. After the application of proposed algorithmic optimizations we obtain a dramatical speedup of the classical methodology without loss of the accuracy. We test our solver the problem with source and sink terms and obtain that the TT-ranks of numerical solution do not grow tremendously even with the insert of the physical effects into the basic Smolushowski coagulation model.