EpODE
Variables
It is a classical method in a program for an iterative process
to renounce to the index number and to work all the time with only two current values, the
first one the previous calculated value, and the second one, the new calculated value.
It we want to see, after the final step, all the computed values, we must store the intermediate
data. In our case, in Yn only some values are those which offers the approximate value.
Based on this observation, in EpODE three vector of method variables must be mentioned, the first one representing the stored values from
one step to another ('starting variables'),
the second one representing the new values which will be calculated and stored ('final variables'),
and the third one (optional) representing the values which will be calculated, but not stored ('intermediate variables').
For example, for a two-step linear method we must define two variables as 'starting variables',
one variable as 'final variable, and none as 'intermediate variable'; for a Runge-Kutta method, we
must define a variable as a 'starting' one, another as a 'final' one, and at least one as an 'intermediate variable'.
Note that, in the computational process, each method variable can represent an $n$-dimensional vector,
if the ODE problem has $n$ equations.
A comment about the source of the method can be also given in the same dialog
box in which the method variables are enumerated.
Example for the method DIRK4