A Fourier interaction picture method using DST/DCT transforms solves parabolic PDEs and SPDEs with non-periodic boundaries, reaching machine precision on the linear heat equation and outperforming polynomial spectral methods for localized and stochastic problems.
Ascher, Steven J
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Non-periodic Fourier propagation algorithms for partial differential equations
A Fourier interaction picture method using DST/DCT transforms solves parabolic PDEs and SPDEs with non-periodic boundaries, reaching machine precision on the linear heat equation and outperforming polynomial spectral methods for localized and stochastic problems.