Abstract
The problem of cubic spline interpolation on the Bakhvalov mesh of functions with region of large gradients is considered. Asymptotically accurate two-side error estimates are obtained for a class of functions with an exponential boundary layer. It is proved that the error estimates of traditional spline interpolation are not uniform in a small parameter, and the error itself can increase indefinitely when the small parameter tends to zero at a fixed number of nodes N. A modified cubic spline is proposed for which uniform estimates of the order O(N −4) have been experimentally confirmed.
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Acknowledgements
The work of Blatov I.A. and Kitaeva E.V. was funded by RFBR, project number 20-01-00650 and the work of Zadorin N.A. was funded by RFBR, project number 19-31-60009.
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Blatov, I., Kitaeva, E., Zadorin, N. (2022). Cubic Spline on a Bakhvalov Mesh in the Presence of a Boundary Layer. In: Badriev, I.B., Banderov, V., Lapin, S.A. (eds) Mesh Methods for Boundary-Value Problems and Applications. Lecture Notes in Computational Science and Engineering, vol 141. Springer, Cham. https://doi.org/10.1007/978-3-030-87809-2_4
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DOI: https://doi.org/10.1007/978-3-030-87809-2_4
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