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Regularisation of Abel's integral equation
Published online by Cambridge University Press: 14 November 2011
Synopsis
Consider the Abel integral operator
where 0 < α < 1. Suppose u is in H1(0, 1) of H1-norm ≦E, and f is an element of L2(0, 1) such that ∥Au – f∥L−2 < ε. We give a regularised approximate solution uβ(f) of the equation
which satisfies
and can be computed simply by performing some integrations. The preceding error estimate can be sharpened by strengthening regularity conditions on u
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 107 , Issue 1-2 , 1987 , pp. 165 - 168
- Copyright
- Copyright © Royal Society of Edinburgh 1987
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