Stability of the coupled leapfrog algorithm. Investigate the stability of the leapfrog algorithm (Equations 5.26) in a simulation; you can reuse your code from Problem 3.5. Use C = 96.8 pF, L = 0.242 µH, and
x = 0.01 m. Launch a Gaussian pulse (described by ?(0, t) = V0e-(t-t0) 2/τ 2 , where τ is the Gaussian pulse half-width, and should be at least 5-10 time steps. Choose t0 such that the pulse slowly ramps up from zero; generally t0 ≥ 3τ is sufficient. Vary the time step ?t, without changing the pulse shape, and investigate the stability of this algorithm. You will find it is most illustrative to look at the case where vp?t/?x is very close to one. How much larger than one can you make the CFL ratio before in instability takes over? How does this depend on the length x of your simulation?