Abstract
The paper concerns the first approach to interval generalized finite differences. The conventional generalized finite differences are of special interest due to the fact that they can be applied to irregular grids (clouds) of points. Based on these finite differences we can compute approximate values of some derivatives (ordinary or partial). Furthermore, one can formulate the generalized finite difference method for solving some boundary value problems with a complicated boundary of a domain. The aim of this paper is to propose the interval counterparts of generalized finite differences. Under the appropriate assumptions the exact values of the derivatives are included in the interval values obtained.
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Acknowledgments
The paper was supported by the Poznan University of Technology (Poland) through Grants No. 02/21/DSPB/3544, 09/91/DSPB/1649.
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Jankowska, M.A., Marciniak, A. (2020). The First Approach to the Interval Generalized Finite Differences. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2019. Lecture Notes in Computer Science(), vol 12044. Springer, Cham. https://doi.org/10.1007/978-3-030-43222-5_34
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DOI: https://doi.org/10.1007/978-3-030-43222-5_34
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