Nodal Equations
Some common nodal configurations are listed in table 5.2 for your reference. On the third column of the table, there is a stability criterion for each nodal configuration. This criterion has to be satisfied for the finite difference solution to be stable. Otherwise, the solution may be diverging and never reach the final solution.
For example, Fo?1/4 for equation 5.71. That is, aDt/(Dx)2 ?1/4 and Dt?(1/4a)(Dx)2. Therefore, the time increment has to be small enough in order to maintain stability of the solution.
This criterion can also be interpreted as that we should require the coefficient for TPm,n in the finite difference equation be greater than or equal to zero.
Question: Why this can be a problem? Can we just make time increment as small as possible to avoid it?