On calculation of asymptotic series in computer algebra systems

S. A. Vasiliev, I. V. Levichev^a, M. D. Malykh<sup>ab

a</sup> Peoples' Friendship University of Russia named after Patrice Lumumba, Moscow
^b Joint Institute for Nuclear Research, Dubna, Moscow region

Abstract: An initial-value problem for a singularly perturbed differential equation is considered. It is shown that not all calculations which are necessary to obtain an asymptotic expansion in an A.B. Vasilyeva series of a given order can be performed in finite form. However, the portion of the calculations that can be performed symbolically is implemented in the Sage computer algebra system. A program for calculating this part in Sage is presented, computational examples are given.

Key words and phrases: singularly perturbed differential equations, asymptotic series, computer algebra.

UDC: 517.928.4

Received: 20.10.2025