Computational Mathematics

Application of a rational approximation in the discontinuous Galerkin method on a semi-infinite interval

M. S. Maksimau^a, S. V. Lemeshevskii<sup>b

a</sup> Institute of Mathematics, National Academy of Sciences of Belarus, 11 Surganava Street, Minsk 220072, Belarus
^b Simmakers, Innovation Centre «Skolkovo», 42 Bolshoj Boulevard, 1 building, Moscow 121205, Russia

Abstract: To solve a problem on an unbounded domain corresponding to the Poisson equation in the spherically symmetric case, a numerical method based on the discontinuous Galerkin method was developed and analysed. To address the unbounded domain, the rational functions were constructed by composing polynomials with an algebraic mapping of a semi-infinite interval. A notable feature of this approach is the use of Sobolev spaces with different weights depending on the derivatives.

Keywords: Discontinuous Galerkin method; semi-infinite interval; Poisson equation; weighted Sobolev spaces; poly- nomial approximation with weights; convergence analysis.

UDC: 519.632.4, 519.624.2

Received: 19.09.2023
Revised: 05.03.2025
Accepted: 05.03.2025