Cache for auxiliary variables in step procedures

[HugoMVale]

The step procedures require a number of auxiliary variables to carry out the corresponding calculations, for instance f1,...f6 in the algorithm below.

module procedure rkf45
real(wp),dimension(me%n) :: f1,f2,f3,f4,f5,f6
...

For each time step, memory to store these variables needs to be allocated and then freed up. For very large ODE sets, these vectors will be huge and the corresponding memory operations can be significantly time consuming.

For optimal efficiency, the corresponding memory should be allocated once and then reused at each step, without repeated (de)allocation. AFAIU, DifferentialEquations.js also does so as well.

In principle, the abstract rk_class could include an allocatable component real(wp), allocatable :: cache(:,:). The cache would be allocated during the instantiation of the concrete method class. Inside the step method, we could then associate:

module procedure rkf45
associate (f1=>me%cache(:,1), f2=>me%cache(:,2), ... )
...

Quite likely, I am missing some important aspects, but I hope the main idea makes some sense.