An Extension of the Product Integration Method to L 1 with Applications in Astrophysics

L Grammont (1) , M Ahues (1) , H Kaboul (1)

1 MMCS - Modélisation mathématique, calcul scientifique

We consider a Fredholm integral equation of the second kind in L 1 ([a, b], C), with a weakly singular kernel. Sucient conditions are given for the existence and uniqueness of the solution. We adapt the product integration method proposed in C 0 ([a, b], C) to apply it in L 1 ([a, b], C), and discretize the equation. To improve the accuracy of the approximate solution, we use dierent iterative renement schemes which we compare one to each other. Numerical evidence is given with an application in Astrophysics. keywords Fredholm integral equation product integration method iterative renement Kolmogorov-Riesz-Fréchet theorem.

Mots clés: iterative refinement; product integration method; Kolmogorov-Riesz-Fréchet theorem.; Fredholm integral equation

Domaines: Mathématiques [math]

L Grammont, M Ahues, H Kaboul. An Extension of the Product Integration Method to L 1 with Applications in Astrophysics. 2015. ⟨hal-01232086⟩