S

I

V

```
"""
Verlet integration is an integration method used to integrate newtons - law of motion. It is frequently used to find trajectories in molecular dynamics simulation.
The function takes `four` inputs viz,
- `f` : the differential equation
- `x0` : the initial condition. This is a Vector with the first element as initial value for position (x_0) and the second initial condition for velocity (v_0)
- `tspan`: is the time span for integration. It is a tuple (initial time, final time)
This functionr returns a tuple (x,t):
- `x` is the solution
- `t` is the array containing the time points
Reference:
- https://www.algorithm-archive.org/contents/verlet_integration/verlet_integration.html
Contributed by: [Ved Mahajan](https://github.com/Ved-Mahajan)
"""
function verlet_integration(f, x0, tspan, Δt = 1.0e-3)
s, e = tspan
N = Int(floor((e - s) / Δt))
x = Vector{Float64}(undef, N)
t = collect(s:Δt:(e-Δt))
x[1] = x0[1]
x[2] = x0[1] + x0[2] * Δt + 0.5 * f(x0[1]) * (Δt)^2
for i in 2:(N-1)
x[i+1] = 2 * x[i] - x[i-1] + f(x[i]) * (Δt)^2
end
return x, t
end
```