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

Authors

  • Mikhail S. Maksimau Institute of Mathematics, National Academy of Sciences of Belarus, 11 Surganava Street, Minsk 220072, Belarus
  • Sergey V. Lemeshevsky Simmakers, Innovation Centre «Skolkovo», 42 Bolshoj Boulevard, 1 building, Moscow 121205, Russia

Keywords:

discontinuous Galerkin method, semi-infinite interval, Poisson equation, weighted Sobolev spaces, polynomial approximation with weights, convergence analysis

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.

Author Biographies

  • Mikhail S. Maksimau, Institute of Mathematics, National Academy of Sciences of Belarus, 11 Surganava Street, Minsk 220072, Belarus

    junior researcher at the department of computational mathematics and mathematical modelling

  • Sergey V. Lemeshevsky, Simmakers, Innovation Centre «Skolkovo», 42 Bolshoj Boulevard, 1 building, Moscow 121205, Russia

    PhD (physics and mathematics); researcher

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Published

2025-05-12

Issue

No. 1 (2025): Journal of the Belarusian State University. Mathematics and Informatics

Section

Computational Mathematics

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How to Cite

[1]
Maksimau, M.S. and Lemeshevsky, S.V. 2025. Application of a rational approximation in the discontinuous Galerkin method on a semi-infinite interval. Journal of the Belarusian State University. Mathematics and Informatics. 1 (May 2025), 23–39.