First-passage time statistics on surfaces of general shape: Surface PDE solvers using Generalized Moving Least Squares (GMLS)

•Computational approaches for First Passage Times (FPTs) and other path-dependent statistics for surfaces of general shape.•Development of high-order surface PDE solvers using meshless methods / Generalized Moving Least Squares (GMLS) approximation.•Methods for general stochastic drift-diffusion dynamics on surfaces and associated Backward-Kolmogorov PDEs.•Methods for handling surfaces with general geometry and topology.•Results for FPTs investigating the roles of surface geometry, drift dynamics, and spatially-dependent diffusivity.