A Spectral Method for Parabolic Differential Equations
It provides a spectral method for a class of parabolic PDEs, but the approach is incremental as it extends existing spectral techniques to a specific problem setting.
The paper presents a spectral method for parabolic PDEs with zero Dirichlet boundary conditions on smooth, bounded domains, achieving spectral convergence for smooth solutions, demonstrated with numerical examples in 2D and 3D.
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 R^2 and R^3.