Year: 2025
Type: article
Abstract: . We address the problem of constructing approximations based on orthogonal polynomials that preserve an arbitrary set of moments of a given function without losing the spectral convergence property. To this aim, we compute the constrained polynomial of best approximation for a generic basis of orthogonal polynomials. The construction is entirely general and allows us to derive structure-preserving numerical methods for partial differential equations that require the conservation of some moments of the solution, typically representing relevant physical quantities of the problem. These properties are essential to capture with high accuracy the long-time behavior of the solution. We illustrate with the aid of several numerical applications to Fokker–Planck equations the generality and the performances of the present approach.
DOI: 10.1137/24m1643086
Authors: Tino Laidin, Lorenzo Pareschi
Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Université de Lille, Laboratoire Paul Painlevé, RAPSODI: Approximations numériques fiables pour les systèmes dissipatifs, University of Ferrara, Heriot-Watt University, Maxwell Institute for Mathematical Sciences
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4391766857