Variable initialization incorrect

[universmile]

The initialization of falm and lfrt are incorrect in Figures 4.69d and 4.70d. This seems to be related to the usage of the smooth function when computing derivatives.

[natema]

One sanity check here is to solve the system with a different method.

[universmile]

The initialization inaccuracy persists after trying different methods.

In the following, we provide the code snippet for Fig. 4.69d.

fig_4_69d_variables = [
    (dlm.fr, 0, 4, "fr"),
    (dlm.falm, 0, 0.1, "falm"),
    (lfd.lfert, 0, 600, "lfert"),
    (lfd.lfd, 0, 80, "lfd"),
    (lfr.lfr, 0, 80, "lfr"),
    (lfr.lfrt, 0, 20, "lfrt"),
]

system = agriculture_historicalrun()
sol_4_69d = WorldDynamics.solve(system, (1900, 2100))
plotvariables(sol_4_69d, (t, 1900, 1970), fig_4_69d_variables, name="Fig. 4.69d", showlegend=true, showaxis=true, colored=true)

After solving the system, we get the following initial values of the flm variable :
sol_4_69d[dlm.falm][1:5] = (0.08, 0.04002382698512611, 0.040040848269282996, 0.040175000234290166)

The origin of the update is coming from the interpolation function :
falm ~ interpolate(pfr, tables[:falm], ranges[:falm])

where

tables[:falm] = (0.0, 0.04, 0.07, 0.09, 0.1) 
ranges[:falm] = (0, 4)

The initial values of pfr are reported below :
sol_4_69d[dlm.pfr][1:4] = (1.0, 1.0110931817510707, 1.0217794925728327, 1.068709296379689)

[natema]

As a sanity check, test if changing the solver as suggested in #60 makes any difference.

[universmile]

Unfortunately, it doesn't.