Adaptive density tracking by quadrature for stochastic differential equations

摘要

Density tracking by quadrature (DTQ) is a numerical procedure for computing solutions to Fokker-Planck equations that describe probability densities for stochastic differential equations (SDEs). In this paper, we extend upon existing trapezoidal quadrature rule DTQ procedures by utilizing a flexible quadrature rule that allows for unstructured, adaptive meshes. We describe the procedure for N-dimensions, and demonstrate that the resulting adaptive procedure can be significantly more efficient than the trapezoidal DTQ method. We show examples of our procedure for problems ranging from one to five dimensions.