We consider approaches to the adaptive choice of an approximation space in the variational-grid method for one-dimensional second order boundary value problems, which allows us to improve approximations and decrease the calculation time in numerical solution. The approaches can be applied to nondegenerate problems, as well as to problems with weak or strong degeneration.
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Yu. K. Dem’yanovich, “Splines of variable approximation order and their wavelet decompositions,” J. Math. Sci. 244, No. 3, 401–418 (2020).
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Translated from Problemy Matematicheskogo Analiza 116, 2022, pp. 47-6
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Dem’yanovich, Y.K. Adaptive Variational-Grid Approximation. J Math Sci 267, 338–361 (2022). https://doi.org/10.1007/s10958-022-06137-8
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DOI: https://doi.org/10.1007/s10958-022-06137-8