  In this paper, the discretization of a nonlinear wave equation whose
nonlinear term is a power function is introduced. The difference equation
derived by discretizing the nonlinear wave equation has solutions which show
characteristics corresponding to the characteristics of the blow-up solutions
for the original equation. The initial value problem for the original equation
has blow-up solutions when a certain condition is met. We prove that when a
similar condition as that of the original solution is met in the initial value
problem for the introduced difference equation, the introduced difference
equation has blow-up solutions having characteristics corresponding to the
characteristics of the blow-up solutions for the original equation.
