Abstract
The weakly singular transfer equation in Astrophysics is settled in the Lebesgue complex Banach space \(L^{1}([a,b], \mathbb{C})\). In this paper, sufficient conditions are given for the existence and uniqueness of the solution and the approximate solution issued from an extension of the product-integration method. The accuracy of the approximate solution is improved through three iterative refinement schemes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Anselone, P.M.: Collectively Compact Operator Approximation Theory and Application to Integral Equations. Prentice-Hall, Englewoods Cliffs, NJ (1971)
Chevallier, L., Pelkowski, J., Rutily, B.: Exact results in modeling planetary atmospheres–I. Gray atmospheres. J. Quant. Spectrosc. Radiat. Transf. 104, 357 (2007)
Acknowledgements
This research has been partially supported by the Indo French Center for Applied Mathematics (IFCAM).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Blanchait, M.A., Kaboul, H. (2017). An L 1-Product-Integration Method in Astrophysics. In: Constanda, C., Dalla Riva, M., Lamberti, P., Musolino, P. (eds) Integral Methods in Science and Engineering, Volume 1. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59384-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-59384-5_1
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-59383-8
Online ISBN: 978-3-319-59384-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)