A spectral method for parabolic differential equations

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.

DOI: 10.1007/s11075-012-9620-8

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@article{Atkinson2012ASM, title={A spectral method for parabolic differential equations}, author={Kendall E. Atkinson and Olaf Hansen and David Da-Kwun Chien}, journal={Numerical Algorithms}, year={2012}, volume={63}, pages={213-237} }