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The explicit method and implicit method are numerical analysis methods used to solve a time-dependent differential equation.
The explicit method
The explicit method calculates the system status at a future time from the currently known system status. The implicit method calculates the system status at a future time from the system statuses at present and future times.
For example, when there is a differential equation
, the
explicit method
expresses it as
.
That is, if you know the state at n, you can calculate the state at n+1.
The implicit method
On the contrary, the
implicit method
has the state at n+1 on the right-hand side as in
. The explicit method is easier to program and can be calculated within a shorter time.
But its stability is so low that you need to use a step size small enough to prevent divergence. On the contrary, the implicit method has high stability and converges if you set proper parameters. But, as you need to solve an equation at every step, it takes a long time to calculate.
As the implicit method can use a sufficiently large step size, it is suitable for solving equations that involve a long time. Also, in non-linear equations such as contact, it is difficult to predict a future from the past state.
So, in these cases, it is recommended that you use the implicit method rather than the explicit method.
For these reasons, RecurDyn , dynamic analysis software, uses the implicit method by default , and uses the explicit method only in some equations.
(Reference: Wikipedia https://en.wikipedia.org/wiki/Explicit_and_implicit_methods )
