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 {\Omega} 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 R^2 and R^3.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2012
- DOI:
- 10.48550/arXiv.1203.6709
- arXiv:
- arXiv:1203.6709
- Bibcode:
- 2012arXiv1203.6709A
- Keywords:
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- Mathematics - Numerical Analysis;
- 65M70
- E-Print:
- 25 pages, 15 figures