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A Spectral Method for Parabolic Differential Equations

Published 30 Mar 2012 in math.NA | (1203.6709v1)

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 R2 and R3.

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