Many scientific, engineering and financial applications require
solving high-dimensional PDEs. However, traditional tensor product
based algorithms suffer from the so called curse of dimensionality.
We shall construct a new sparse spectral method for
high-dimensional problems, and present, in particular,
rigorous error estimates as well as efficient numerical algorithms for
We shall also propose a new weighted weak formulation for
the Fokker-Planck equation of FENE dumbbell model, and prove its