Explicit and Implicit Methods
The solution of Eq. (3.4) takes the form of a “marching” procedure (or scheme) in steps of time.
We know the dependent variable at all at a time level from given initial conditions. Examining Eq. (3.4) we see that it contains one unknown, namely .
Thus, the dependent variable at time is obtained directly from the known values of and
This is a typical example of an explicit finite difference method.
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at a time level from given initial conditions. Examining Eq. (3.4) we see that it contains one unknown, namely 
. 
is obtained directly from the known values of 
and 
