Solving singular integral equations with orthogonal rational functions - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail (Working Paper) Année : 2024

Solving singular integral equations with orthogonal rational functions

Bernhard Beckermann
  • Fonction : Auteur
  • PersonId : 1337437
Ana C Matos
  • Fonction : Auteur
  • PersonId : 1337438

Résumé

We suggest a new numerical method of solving the signed equilibrium with external field in logarithmic potential theory on a union of distinct real intervals. A reformulation of our problem leads us to a system of integral equations with a weakly singular Cauchy kernel. We then recall a polynomial spectral method and its error analysis, and suggest a new spectral method using orthogonal rational functions in order to solve our problem. Choosing appropriate and explicitly given poles allows to speed up computation. Such techniques have been exploited also in the famous adaptative multipole algorithm for particle simulations [8] or more recently for solving the Laplace equation [28].
Fichier principal
Vignette du fichier
SingEquaORF_BB_v4_bis.pdf (292.66 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04402726 , version 1 (18-01-2024)

Identifiants

  • HAL Id : hal-04402726 , version 1

Citer

Bernhard Beckermann, Ana C Matos. Solving singular integral equations with orthogonal rational functions. 2024. ⟨hal-04402726⟩
41 Consultations
82 Téléchargements

Partager

Gmail Mastodon Facebook X LinkedIn More