The paper investigates the improvement of methods for computing the concentration of nanoparticles in transparent liquids under the action of laser radiation. The exact solution of the third boundary value problem for the Einstein–Fokker–Planck equation is analyzed, the direct use of which in the Maple computer algebra system leads to computational instabilities at large values of the transfer parameter. A solution to the problem of unstable numerical calculations at high values of dimensionless parameters, leading to significant distortions of the result, is presented. The key result is to expand the working range of the transfer parameter and ensure the correct asymptotic behavior of the solution. Numerical experiments have confirmed the effectiveness of the proposed approach, which makes it a valuable tool for modeling and optimizing the processes of laser separation of nanoparticles.

Keywords: nanosuspension, laser radiation, concentration of nanoparticles, continuity equation, third boundary value problem, computer calculations, Maple