How to compute the perihelion precession of Earth's orbit?
For simulation only, you should be able to show it by simple code as following:
$$
\vec{a}_t = - \frac{GM}{r_t^2} \hat{r} \\
\vec{v}_{t+1} = \vec{v}_t + \vec{a}_t \Delta t \\
\vec{r}_{t+1} = \vec{r}_t + \vec{v}_t \Delta t 
$$
where $t$ is time step, $\vec{a}$ is acceleration, $\vec{v}$ is velocity, $\vec{r}$ is position, $\hat{r}$ is a unit vector in radial direction from the origin (set the Sun at the origin), $G$ is gravitational constant, $M$ is Sun mass in this case, and $\Delta t$ is size of time step. You will have to play around with the initial values and step size to get certain orbit representing the case. To make it more real, you derive the initial values from the real parameters, if known.