try DAEproblem

Author: ChrisRackauckas

benchmarks/DAE/LinearDAE.jmd

@@ -79,6 +79,7 @@ rlc_eqs = E_rlc * Dx ~ A_rlc * x + B_rlc .* u(t)
 # Problems using constant voltage input
 rlc_prob = ODEProblem(rlc_sys, [i_R => 0.0, v_C => 0.0], (0.0, 1e-3))
 rlc_static_prob = ODEProblem{false}(rlc_sys, SA[i_R => 0.0, v_C => 0.0], (0.0, 1e-3))
+rlc_dae_prob = DAEProblem(rlc_sys, [i_R => 0.0, v_C => 0.0, D(i_R) => 0.0, D(i_L) => 0.0], [], (0.0, 1e-3))
 ```
 
 ## Index-2 DAE: Two Interconnected Rotating Masses  
@@ -123,6 +124,7 @@ masses_eqs = E_masses * Dx ~ A_masses * x + B_masses * u(t)
 # Problems using torque inputs
 masses_prob = ODEProblem(masses_sys, [], (0.0, 1.0))
 masses_static_prob = ODEProblem{false}(masses_sys, SA[], (0.0, 1.0))
+masses_dae_prob = DAEProblem(masses_sys, [D(θ2) => 0.0, D(ω1) => 0.0], [], (0.0, 1.0))
 ```
 
 ## Index-2 DAE: RL Network
@@ -163,6 +165,7 @@ rl_eqs = E_rl * Dx ~ A_rl * x + B_rl .* u(t)
 # Problems using current source input
 rl_prob = ODEProblem(rl_sys, [v_L => 1.0], (0.0, 1.0))
 rl_static_prob = ODEProblem{false}(rl_sys, SA[v_L => 1.0], (0.0, 1.0))
+rl_dae_prob = DAEProblem(rl_sys, [v_L => 1.0, D(v_L) => 0.0, D(i1) => 0.0], [], (0.0, 1.0))
 ```
 
 ## Index-3 DAE: Cart Pendulum
@@ -212,6 +215,7 @@ cart_eqs = E_cart * Dx ~ A_cart * x + B_cart .* u(t)
 # Problems using force input
 cart_prob = ODEProblem(cart_sys, [dy_cart => 0.0, y_cart => 0.0], (0.0, 1.0))
 cart_static_prob = ODEProblem{false}(cart_sys, SA[dy_cart => 0.0, y_cart => 0.0], (0.0, 1.0))
+cart_dae_prob = DAEProblem(cart_sys, [dy_cart => 0.0, y_cart => 0.0], [], (0.0, 1.0))
 ```
 
 ## Index-3 DAE: Electric Generator
@@ -254,6 +258,7 @@ gen_eqs = E_gen * Dx ~ A_gen * x + B_gen .* u(t)
 # Problems using torque input
 gen_prob = ODEProblem(gen_sys, [ω_gen => 1.0], (0.0, 1.0))
 gen_static_prob = ODEProblem{false}(gen_sys, SA[ω_gen => 1.0], (0.0, 1.0))
+gen_dae_prob = DAEProblem(gen_sys, [ω_gen => 1.0, D(ω_gen) => 0.0], [ω_gen => 0.0], (0.0, 1.0))
 ```
 
 ## Index-3 DAE: Damped Mass-Spring System
@@ -326,6 +331,7 @@ spring_static_prob = ODEProblem{false}(spring_sys, SA[λ_spring => 0.0, v1_sprin
 # Generate reference solutions for all systems using robust methods
 rlc_ref = solve(rlc_prob, Rodas5P(), abstol=abstol_ref, reltol=reltol_ref)
 rlc_static_ref = solve(rlc_static_prob, Rodas5P(), abstol=abstol_ref, reltol=reltol_ref)
+rlc_dae_ref = solve(rlc_dae_prob, IDA(), abstol=abstol_ref, reltol=reltol_ref)
 
 masses_ref = solve(masses_prob, Rodas5P(), abstol=abstol_ref, reltol=reltol_ref)
 masses_static_ref = solve(masses_static_prob, Rodas5P(), abstol=abstol_ref, reltol=reltol_ref)