[sage-support] 'unable to simplify to float approximation' error in Logistic equation
I am having some troubles to get the logistic equation from its
differential form. For example:
sage: tau = var('tau') # proportionality constant
sage: k = var('k') # max population size
sage: t = var('t') # independent variable
sage: p = function('p', t) # dependent variable
sage: myode = tau*diff(p,t) == p*(1-p/k)
sage: sol(t) = desolve(de=myode, ivar=t, dvar=p)
sage returns:
-tau*log(-k + p(t)) + tau*log(p(t)) == c + t
Now, when I try to show the solution to the equation:
sage: plot(sol.subs(tau=20, k=10, c=1), 0, 100)
i've got the following error:
verbose 0 (4075: plot.py, generate_plot_points) WARNING: When plotting,
failed to evaluate function at 200 points.
verbose 0 (4075: plot.py, generate_plot_points) Last error message:
'unable to simplify to float approximation'
I would appreciate some help here.
Thanks in advance
Jose
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Re: [sage-support] 'unable to simplify to float approximation' error in Logistic equation
The problem is that the solution that desolve returns:
sage: myode = tau*diff(p,t) == p*(1-p/k)
sage: sol(t) = desolve(de=myode, ivar=t, dvar=p)
sage returns:
-tau*log(-k + p(t)) + tau*log(p(t)) == c + t
isn't in an easy enough form for plot to display. You're setting
sol(t) not to an expression but to an equation, and a non-trivial one.
(You might be able to make implicit_plot work with some tweaking but
I'm lazy. :^)
We can fix that, though. Try something like
tau = var('tau') # proportionality constant
k = var('k') # max population size
t = var('t') # independent variable
p = function('p', t) # dependent variable
myode = tau*diff(p,t) == p*(1-p/k)
sol = desolve(de=myode, ivar=t, dvar=p)
sol = sol.simplify_full() # simplify_log would suffice
sol_p(t) = solve(sol,p,solution_dict=True)[0][p] # make a function
from the solution
plot(sol_p.subs(tau=20, k=10, c=1), 0, 100)
Doug
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