The finite difference equation, based on second order in time and second order in space approximations, is

Equation 47 is the discrete approximation to the
wave equation shown in Equation 1. The choice of the
right hand side (RHS)
time value as **n** describes an explicit time marching scheme
where the **n+1** is a function of **n** and **n-1**:

If the RHS was
chosen to have an **n+1** time value, the resulting difference equation
would have been implicit. The implicit form requires solving a
system of equations at each time step and has a significant
increase in computational complexity.
The explicit form
Equation 48
is used here with good results, and in a later section
the stability of the explicit method is considered.