Abstract
We study the integral equation
where \(f \in C[0,1] \cap C^{m}(0,1)\), \(a,b \in C^{m}([0,1] \times (0,1))\), \(m \in \mathbb{N} = \left \{1,2,...\right \}\). By C m(Ω) is meant the set of all m times continuously differentiable functions on Ω. By C[0, 1] is meant the Banach space of continuous functions \(u: [0,1] \rightarrow \mathbb{R} = (-\infty,\infty )\) with the usual norm \(\left \|u\right \|_{\infty } = \left \{\max \left \vert u(x)\right \vert: 0 \leq x \leq 1\right \}\).Denote by T the integral operator of equation (37.1):
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Acknowledgements
This work was supported by Estonian Science Foundation Grant No 9104 and by the institutional research funding IUT20-57 of the Estonian Ministry of Education and Research.
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Orav-Puurand, K., Pedas, A., Vainikko, G. (2015). A Collocation Method Based on the Central Part Interpolation for Integral Equations. In: Constanda, C., Kirsch, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16727-5_37
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DOI: https://doi.org/10.1007/978-3-319-16727-5_37
Publisher Name: Birkhäuser, Cham
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