The generalized local maximum principle for a difference operator $L_h$ asserts that if $L_hu(x) > 0$ then $\Gamma u$ cannot attain its positive maximum at the net ...

Finite difference methods have become a cornerstone in the simulation of seismic wave propagation, providing a robust numerical framework to approximate the differential equations that govern seismic ...

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 ...