  We prove convergence of a finite difference scheme to the unique entropy
solution of a general form of the Ostrovsky--Hunter equation on a bounded
domain with non-homogeneous Dirichlet boundary conditions. Our scheme is an
extension of monotone schemes for conservation laws to the equation at hand.
The convergence result at the center of this article also proves existence of
entropy solutions for the initial-boundary value prob lem for the general
Ostrovsky--Hunter equation. Additionally, we show uniqueness using
Kru\v{z}kov's doubling of variables technique. We also include numerical
examples to confirm the convergence results and determine rates of convergence
experimentally.
