Fig. 2

Relative error \(\eta\) of the momentum vector \(\varvec{u}=(u_x,u_y)\) and position vector \(\varvec{r}=(x,y)\) from the theoretical solution as a function of \(\Delta t\) for the present integrators with the combination of the tangent function and different integrators. The circle, triangle, square, and x-mark show the results with Euler, trapezoidal, Heun3, and RK4 integrators, respectively