  In neuroscience, the distribution of a decision time is modelled by means of
a one-dimensional Fokker--Planck equation with time-dependent boundaries and
space-time-dependent drift. Efficient approximation of the solution to this
equation is required, e.g., for model evaluation and parameter fitting.
However, the prescribed boundary conditions lead to a strong singularity and
thus to slow convergence of numerical approximations. In this article we
demonstrate that the solution can be related to the solution of a parabolic PDE
on a rectangular space-time domain with homogeneous initial and boundary
conditions by transformation and subtraction of a known function. We verify
that the solution of the new PDE is indeed more regular than the solution of
the original PDE and proceed to discretize the new PDE using a space-time
minimal residual method. We also demonstrate that the solution depends
analytically on the parameters determining the boundaries as well as the drift.
This justifies the use of a sparse tensor product interpolation method to
approximate the PDE solution for various parameter ranges. The predicted
convergence rates of the minimal residual method and that of the interpolation
method are supported by numerical simulations.
