Abstract
We present a spectral method for parabolic partial differential equations with zero Dirichlet boundary conditions. The region Ω for the problem is assumed to be simply-connected and bounded, and its boundary is assumed to be a smooth surface. An error analysis is given, showing that spectral convergence is obtained for sufficiently smooth solution functions. Numerical examples are given in both ℝ2 and ℝ3.
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Atkinson, K., Hansen, O. & Chien, D. A spectral method for parabolic differential equations. Numer Algor 63, 213–237 (2013). https://doi.org/10.1007/s11075-012-9620-8
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DOI: https://doi.org/10.1007/s11075-012-9620-8