Is ode15i correct for this situation?

Can someone tell me if this is the correct approach and if so provide suggestions to get this to solve?

I have a system that is characterized by 3 equations in this form:

y'(1) - y(2) = 0

y'(2) + fun1(y(1),y(2),y(3)) = 0

fun2(y(2)) + fun3(y(3)) = 0

The 3 functions are not linear. Since this is a DAE system and since it was most convenient to arrange them as f(t,y,y’) = 0, I used ode15i. Is this correct? The solution fails either at t=0 or some later time with a singular matrix warning depending on choice of parameters.

I differentiated the 3rd equation hoping to have a system of ODEs instead of DAEs. For my functions, the system takes this form:

y'(1) - y(2) = 0

y'(2) + fun1(y(1), y(2), y(3)) = 0

fun2(y'(2)) + fun3(y(3), y'(3)) = 0

Since both y'(2) and y'(3) appear in the 3rd equation, am I stuck with a fully implicit situation and back to using only ode15i? This formulation fails at t=0 with a singular matrix warning.

Any insight appreciated.

[Torsten]

Use

y'(3) = -d/dy(2)(fun2(y(2))) * (-fun1(y(1),y(2),y(3))) / d/dy(3)(fun3(y(3)))

as third equation.

Best wishes

Torsten.

[Tom Mallin]

Torsten, can you show how you arrived at your suggestion for the 3rd equation?

[Torsten]

Implicit differentiation of equation (3) with respect to t:

fun2(y(2)) + fun3(y(3)) = 0 ->
[d/dy(2) (fun2(y(2)))]*dy(2)/dt + [d/dy(3) (fun3(y(3)))]*dy(3)/dt = 0 ->
dy(3)/dt = - [d/dy(2) (fun2(y(2)))]*dy(2)/dt / [d/dy(3) (fun3(y(3)))] -> (from equation (2))
dy(3)/dt = - [d/dy(2) (fun2(y(2)))]*(-fun1(y(1), y(2), y(3)))/ [d/dy(3) (fun3(y(3)))]

Best wishes

Torsten.

[Tom Mallin]

Torsten, your suggestion is exactly what I've done to change the first formulation into the second. My fun2 and fun3 were meant to be different in the 2 formulations. I thought you were starting with the 3rd equation in the 2nd formulation and differentiating again which didn't make sense.

In any case, I think ode15i is proper for solving formulation 1 and ode45 is proper for formualation 2. Neither are working so I suspect some other issue.