swMATH ID: 25990
Software Authors: Askham, T.
Description: A stabilized separation of variables method for the modified biharmonic equation. The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier-Stokes equations. We develop a separation of variables representation for this equation in polar coordinates, for either the interior or exterior of a disk, and derive a new class of special functions which makes the approach stable. We discuss how these functions can be used in conjunction with fast algorithms to accelerate the solution of the modified biharmonic equation or the ”bi-Helmholtz” equation in more complex geometries.
Homepage: https://zenodo.org/record/997157#.W7Ouga35x_8
Keywords: separation of variables; modified biharmonic equation; special functions; integral equation; fast multipole method
Related Software: FMMLIB2D; DLMF; linequad; FINUFFT; rbf_qr; Julia; FFTPACK; EISPACK
Cited in: 5 Publications

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