Merge x and xf into single inout argument in step procedures

[HugoMVale]

Currently, step methods have an interface like so:

subroutine step_func_fixed(me,t,x,h,xf)
!! rk step function for the fixed-step methods.
import :: rk_fixed_step_class,wp
implicit none
  class(rk_fixed_step_class),intent(inout) :: me
  real(wp),intent(in)                      :: t  !! initial time
  real(wp),dimension(me%n),intent(in)      :: x  !! initial state vector
  real(wp),intent(in)                      :: h  !! time step \( |\Delta t| \)
  real(wp),dimension(me%n),intent(out)     :: xf !! final state vector
end subroutine step_func_fixed

There is no need for a separate arguments x intent(in) and xf, intent(out). They can be merged into a single argument x, intent(inout), thereby avoiding a redundant state vector.

For instance, for Euler:

module procedure euler
associate (f1 => me%funcs(:,1))
    call me%f(t,x,f1)
    x = x + h*f1
end associate
end procedure euler

The change should be more or less straightforward for all methods expressed in the classical the rk form. For SSP and LS methods, one registry will probably have to be added because the implementations were already making use of the extra x. I can help with that; just let me know what you think.

[jacobwilliams]

Yes, that seems reasonable!