  Approximate weak solutions of the Fokker-Planck equation can represent a
useful tool to analyze the equilibrium fluctuations of birth-death systems, as
they provide a quantitative knowledge lying in between numerical simulations
and exact analytic arguments. In the present paper, we adapt the general
mathematical formalism known as the Ritz-Galerkin method for partial
differential equations to the Fokker-Planck equation with time-independent
polynomial drift and diffusion coefficients on the simplex. Then, we show how
the method works in two examples, namely the binary and multi-state voter
models with zealots.
