Titre :

Solving singular integral equations with orthogonal rational functions

Auteur(s) :

Beckermann, Bernhard [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Matos, Ana [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Mot(s)-clé(s) en anglais :

equilibrium problems singular integral equations orthogonal rational functions spectral methods
equilibrium problems
singular integral equations
orthogonal rational functions
spectral methods

Discipline(s) HAL :

Mathématiques [math]/Analyse numérique [math.NA]

Résumé en anglais : [en]

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 ...
Lire la suite >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].Lire moins >

Langue :

Anglais

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL