Consider an initial value problem (IVP) $y'=f(t,y)$ with the initial value given by $y(t=0) = 0$.
If I need to find $y(t^*)$, hence finding the path for $y$ in $t \in [0,t^*]$ and $t^*<0$; is the problem then still an initial value problem? In other words can you go back in time in IVP.
The reason I ask is that I have an algorithm where in each step I need to solve for different $t^*$. I intend to use
solve_ivp in Python which is based on Runge-Kutta 45 method and I want to know if there are any theoretical contradictions when I apply RK45.
I know that if I will use Eulers method then there is no problem. But what about RK45. Will I get the desired result.