Ordinary differential equations (ODEs) and difference equations serve as complementary tools in the mathematical modelling of processes evolving in continuous and discrete time respectively. Together ...

Finite difference methods for degenerate linear and (certain) nonlinear elliptic and parabolic equations are analyzed from a probabilistic point of view, and probabilistic methods are used to show ...

A stable finite-difference scheme for the wave equation may possess features not shared by the underlying partial differential equation. These discrepancies are explored; in particular, an asymptotic ...