An Extension of the Product Integration Method to L1 with Applications in Astrophysics. Issue 6 (1st November 2016)

• Record Type: Journal Article
• Authors: Grammont, Laurence; Ahues, Mario; Kaboul, Hanane
• Is Part Of: Mathematical modelling and analysis. Volume 21:Issue 6(2016)
• Page Start: 774
• Page End: 793
• Publication Date: 2016-11-01
• Subjects: Fredholm integral equation -- product integration method -- iterative refinement -- Kolmogorov-Riesz-Fréchet theorem; 45B05 -- 45A05 -- 45E99; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2016.1243590
• Languages: English
• ISSNs: 1392-6292

Abstract

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.