Efficient numerical approximation of a non-regular Fokker-Planck equation associated with first-passage time distributions
The Fokker-Planck equation on a one-dimensional spatial domain with discontinuity between initial and boundary data and time-dependent boundaries is solved numerically. The equation is transformed first into an equation on a rectangular time-space domain. It was shown that the solution of a corresponding equation with a suitable constant drift function, whose solution is explicitly available as a fast converging series expansion, captures the singularity present in the solution for a variable drift function. The equation for the difference of both these solutions, which is thus more regular than both terms, is solved with a minimal residual method. In order to efficiently solve Fokker-Planck equations that depend on multiple parameters, the authors apply a sparse tensor product interpolation method that can be shown to converge at a subexponential rate as a function of the number of interpolation points. The predicted convergence rates of the minimal residual method and that of the interpolation method are supported by numerical simulations.
scientific article; zbMATH DE number 7621789
scientific article