'Freezing' time by setting initial time value

[lamorton]

Related to #998. If you declare the independent variable as a parameter instead of a variable, it's usually not a problem. However, if the independent variable is then captured in the parameters list, it leads to an error message (ERROR: ArgumentError: Sym{Real, Base.ImmutableDict{DataType, Any}}[t] are missing from the variable map.) suggesting that you need to provide an initial/fixed value for t. However, if you do that, then you shadow the independent variable with a parameter, as far as any inhomogenous equations are concerned. That leads to incorrect output (ie, assuming t is 0 for all times.)

using ModelingToolkit, DifferentialEquations
pars = @parameters((A, t)) #Maybe this is the erroneous line?
vars = @variables((u2(t), u1(t)))
der = Differential(t)
eqs = [
  der(u1) ~ u2,
  0 ~ u2 - A  * t,
]
sys = ODESystem(eqs,t,vars,pars)

params = Dict(
  A => 12.0,
  t => 0.0, #Or maybe this is the problem?
)
initialValues = [
  u1 => 0.0,
  u2 => 0.0,
]

sys_simple = structural_simplify(sys)
tspan = (0.0, 1.0)
problem = ModelingToolkit.ODEProblem(reducedSystem , initialValues, tspan, params)

sol = solve(problem, Rodas5()) #Result is all zeros

Possible resolutions:

• Assert that the independent variable is not in the set of parameters
• Make the error message for missing parameter values and/or initial values more specific
• Change the substitution process so that the independent variable cannot be shadowed?

[ChrisRackauckas]

Assert that the independent variable is not in the set of parameters

Yeah, it really shouldn't be. That is kind of a quirk of history that needs to be corrected.