Pseudospectral numerical algorithms

To summarize, pseudospectral algorithms are easier to program. On the other hand, the Galerkin methods are more accurate for small N and are easier to understand and manipulate for theoretical purposes such as perturbatirMi theory. Perhaps, the Galerkin methods are more robust for difficult problems. For numerical purposes, however, there is not much to choose between them [1]. 

Sophisticated numerical techniques have been devised to study this standard model within mean field approximation. They exploit that the mean field problem of a Gaussian chain in an external field can be described by a modified diffusion equation in an external field [60]. The latter leads to a partial differential equation that can be solved by efficient computational techniques. Advanced real-space, spectral, and pseudospectral algorithms have been devised to this end [28, 78-80]. ... 

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