edu.ucar.opensky::articles:10277 UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact 2025-12-26T14:57:31.232226 ISO 19115-2 Geographic Information - Metadata - Part 2: Extensions for Imagery and Gridded Data ISO 19115-2:2009(E) https://n2t.org/ark:/85065/d7dj5g1h Comparisons between pseudospectral and radial basis function derivative approximations 2010-01-01T00:00:00Z publication https://n2t.org/ark:/85065/d7dj5g1h https://doi.org/10.1093/imanum/drn064 Fornberg, B. author Flyer, Natasha author Russell, J. author UCAR/NCAR - Library publisher Fourier-based pseudospectral (PS) methods have been used since the 1970s for obtaining spectrally accurate solutions to PDEs in periodic geometries. Radial basis functions (RBFs) were introduced about the same time for interpolation on scattered nodes in irregular geometries. As was later recognized, they can also be used for accurate numerical solution of PDEs. Although the main strength of RBFs lies in their outstanding geometric flexibility, offering possibilities of spectral accuracy also over irregularly shaped finite domains, it is still of interest to compare them against Fourier-based PS methods in the extremely simple geometries (infinite or periodic domains) where the latter can also be used. Mostly by means of heuristic arguments and graphical illustrations based on Fourier analysis and numerical experiments, we show that there are notable differences (more pronounced in increasing numbers of dimensions) in how the two spectral approaches approximate derivatives. UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact PDF Text theme Resource Type 2016-01-01T00:00:00Z publication An edited version of this paper was published by the IMA. Copyright 2010 IMA. None eng geoscientificInformation