Large initial values in DAE system

Specific Domains Modelling & Simulations
1

Hi all,

I am trying to solve a DAE system using DifferentialEquations.jl where initial values can be relatively large (order 1e22). The MWE below (algebraic equations omitted) solves fine up to n0[1] = 1e15 but throws an IDAS error when I increase this value further. Therefore I was wondering whether there is any fundamental limitation of usable n0 in this example, and if so, why?

using DifferentialEquations
using Plots

function func(r,dn,n,param,t)
    r[1] = -n[1] + n[2] - dn[1]
    r[2] = +n[1] - n[2] - dn[2]
end

n0 = [1.0e15, 0]
dn0 = [0.0, 0.0]
diff_var = [true, true]
tspan = [0.0, 1e1]
param = []
prob = DAEProblem(func,dn0,n0,tspan,param,differential_vars=diff_var)

sol = solve(prob)
Plots.plot(sol)

Here the full error message:

[IDAS ERROR]  IDACalcIC
  The residual routine or the linear setup or solve routine had a recoverable error, but IDACalcIC was unable to recover.

In principle I could probably get around this by using a lower n0 and scaling other parameters accordingly, but with a number of algebraic equations that require scaling this can become a little troublesome.