A Spectral Method for Parabolic Differential Equations

Details A Spectral Method for Parabolic Differential Equations A Spectral Method for Parabolic Differential Equations

2012-03-30

arxiv.org/abs/1203.6709v1

Mathematics

Numerical Analysis

25 pages, 15 figures

Scientific paper

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.

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