What's the difference between using and not using inline integration in Dymola?

Question

I am trying to make it clear the difference between using inline integration and not using inline integration during simulation in Dymola.
Here is the basic procedure of the DASSL algorithm:

I find the following summary about the inline integration technique:

To summarise, inline integration harnesses the symbolic manipulation of Dymola to insert discretization expressions, representing the numerical integration algorithms, into the differential-algebraic equation (DAE) model to be solved. In effect, the inserted discretization expressions (representing the numerical integration algorithms) are solved “inline” with the model, rising to the name of the technique. The upshot is a DAE which is easier to solve numerically, thus leading to a shorter solve time.

1. as to the part of insert discretization expression into DAE model to be solved, I think DASSL does the same thing, as shown in the above screenshot, DASSL would insert the expression of y=h*der(y)+old(y) into the original DAE.
2. but what does it mean by inserted discretization expressions are solved inline with the model? In the DASSL algorithm, I just use Newton Method to solve the nonlinear equations of f(y-old(y)/h,y,t)=0, it seems natural. So what would happen if I use the inline integration method?

Answer 1

There is currently no inline DASSL in Dymola. For non-inline explicit Euler the C-code contain (well, with different variable names):

der(y)=f(y)

(and there is some integration code that computes y(t+h)=y(t)+h*der(y) ). For inline explicit Euler the the C-code contain:

y(t+h)=y(t)+h*f(y)

The main benefits are:

• For implicit methods where each system of equation can be solved separately.
• It can be used (as an FMU/S-function) in other tools that don't themselves support the integration method.