An Extension of the Product Integration Method to L1 with Applications in Astrophysics. Issue 6 (1st November 2016) - Grammont, Laurence; Ahues, Mario; Kaboul, Hanane
Abstract: A Fredholm integral equation of the second kind in L 1 ([a, b], ℂ) with a weakly singular kernel is considered. Sufficient 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 different iterative refinement schemes which we compare one to each other. Numerical evidence is given with an application in Astrophysics.