An Extension of the Product Integration Method to L1 with Applications in Astrophysics

Abstract

A Fredholm integral equation of the second kind in L1([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 C0 ([a, b], C) to apply it in L1 ([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.

Keywords

• Fredholm integral equation
• product integration method
• iterative refinement
• Kolmogorov-Riesz-Frechet theorem