  We develop a hybrid scheme based on a finite difference scheme and a
rescaling technique to approximate the solution of nonlinear wave equation. In
order to numerically reproduce the blow-up phenomena, we propose a rule of
scaling transformation, which is a variant of what was successfully used in the
case of nonlinear parabolic equations. A careful study of the convergence of
the proposed scheme is carried out and several numerical examples are performed
in illustration.
