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

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.