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A fully discrete difference scheme is constructed with space discretization by compact difference method.
The fully discrete scheme (14) is unconditionally stable.
The semi-discrete and fully discrete schemes are established.
Now, we consider the convergence of the fully discrete scheme.
Then, a fully discrete difference scheme is derived.
Fully discrete versions are obtained with appropriate Runge Kutta solvers.
Conditions for fully discrete stability is furthermore established.
Further, it is shown that the fully discrete CNFVE formulation is better than the fully discrete FVE formulation with the first-order accuracy in [19], thus validating the feasibility and efficiency of the fully discrete CNFVE formulation.
It is shown that the fully discrete CNFVE formulation is far better than the fully discrete FVE formulation with the first-order accuracy in time.
Further, it is shown that the fully discrete CNFVE formulation is better than the fully discrete FVE formulation with the first-order accuracy in time (see [19]).
Therefore, the fully discrete CNFVE formulation is far better than the fully discrete FVE formulation with the first-order accuracy in time in [19].
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