- Published 2012 in Numerical Algorithms

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.

@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}
}