I’m trying to solve the following DAE:
\begin{cases}
i_R=C \displaystyle \frac{dV_o}{dt}
\\
i_R= \displaystyle \frac{V_{in}(t)-V_o-nV_T \ln \displaystyle (1+\displaystyle \frac{i_R}{I_s}) }{R}
\end{cases}
The solution obtained from a simulator is:
Nevertheless, we want to solve the model with DifferentialEquations.jl, and I’ve tried with the following code:
using DifferentialEquations, Plots
f = 10E3
ω = 2*π*f
n = 1
C = 0.01E-6
VT = 25E-3
IS = 1E-6
A = 1.0
R = 10E3
function func(out, du, u, p, t)
V0, IR = u
dV0, _ = du
out[1] = C*dV0 - IR
out[2] = (A*sin(ω*t) - V0 - n*VT*log(1+IR/IS)) - R*IR
end
B = A*ω/R/(1+n*VT/R/IS)
u₀ = [0, 0.0] # V0, IR
du₀ = [0, B] # dV0, dIR
dvars = [true, false]
tspan = (0, 2E-3)
prob = DAEProblem(func, du₀, u₀, tspan, differential_vars=dvars);
It gives the following error:
sol = solve(prob)
DomainError with -0.33407903800223493:
log will only return a complex result if called with a complex argument. Try log(Complex(x)).
What do you suggest to tackle this problem?
