Solving a higher index DAE formulating it as a DAEProblem

I’m trying to solve a higher index DAE (say in my case index 3) system of equations formulating it directly as a DAEProblem without converting it into an ODEProblem.

Going through the documentation I could find only examples that utilizes index reduction in modelingtoolkit.jl and further solving it as an ODEProblem. I’m looking further into solving it as a DAEProblem.

Is there a possible way to do that ? If so, with what solvers ?

Here is a simple case of equations of pendulum where we encounter a DAE system of index 3. The code below gives me an error message ‘convergence failure’ as I have directly attempted to solve it without index reduction. Can I get any possible help to reduce its index and further solving it as a DAEProblem ?

using DifferentialEquations, ModelingToolkit  
using  LinearAlgebra, DASKR

function f(out, da, a, p, t)    
   (L, m, g) = p
   u, v, x, y, T = a
   du, dv, dx, dy, dT = da
   out[1] = x*T/(m*L) - du
   out[2] = y*T/(m*L) - g - dv
   out[3] = u - dx
   out[4] = v - dy
   out[5] = u^2 + v^2 - L^2

u0 = zeros(5)
u0[3] = 1.0
du0 = zeros(5)
du0[2] = 9.81

p = [1,1,9.8]
tspan = (0.,100.)
differential_vars = [true, true, true, true, false]

prob = DAEProblem(f, du0, u0, tspan, p, differential_vars = differential_vars)

Thanking in advance…

Just call DAEProblem from ModelingToolkit on the sys. It can generate an ODEProblem, ODAEProblem, and the DAEProblem forms. You’ll need the MTK structural simplification to do the index reduction.

Great Thanks. It worked…