An Extension of the Product Integration Method to L 1 with Applications in Astrophysics
نویسنده
چکیده
We consider a Fredholm integral equation of the second kind in L1([a, b],C), with a weakly singular kernel. 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-Fréchet theorem.
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