Euler method versus RK45?

[WeileiZeng]

In the code, the Euler method with fixed step length is implemented as the solver for the master equation. Why Runge Kutta method with 4th order accuracy and adjustable step length not provide a higher accuracy?

This is mentioned in the paper but I haven't get the point.

In my impression, when the system reach the bifurcation point, most spins start moving towards a stable solution, with a very small momentum. This process takes time. A more accurate solver with smaller step length should be helpful in this procedure, reducing random flips by noise and speeding up stabilizing the system.

[bqth29]

Hi @WeileiZeng and thanks for reaching out!

Indeed the RK method could be tried for the SB algorithm. It would be a relevant new feature in the solver, and the choice could be given to users between Euler or RK symplectic integrators.

To be honest, we only implemented Euler at the moment since this method was extensively described in the original papers. But RK is definitely worth the experiment.

We can use this issue as the starting point for the integration of the RK method. We'll first have to properly write down the equations and then we can start adding the method in the codebase.

If you wish to collaborate to the code you or the mathematical background you are welcome 😄

All the best!