odeToVectorField: Unable to convert the initial value problem to an equivalent dynamical system.

Could anyone help me with following Matlab codes. Why do they generate error and how to fix them?

syms t v1(t) v2(t) v3(t)

equ=[v1(t) == 10e-03*sin(2*pi*1e08*t);...
    1e-00*(v2(t)-v1(t))+1e-03*(v2(t)-v3(t))+1e-09*diff(v2(t)-v3(t),t) == 0;...
    1e-03*(v3(t)-v2(t))+1e-09*diff(v3(t)-v2(t),t)+1e-03*v3(t) == 0];

Vect=odeToVectorField(equ);

[madhan ravi]

https://www.mathworks.com/help/symbolic/odetovectorfield.html#bvlqf2q-6 , could you upload the latex form of the equations ?

[S H]

How is that neccessary? Can you explain?

Answer 1

[Stephan]

Hi,

i deleted my first answer - cause your comment brought me to a new thought - DAE:

syms t v1(t) v2(t) v3(t)
eq1 = v1(t) == 10e-03*sin(2*pi*1e08*t);
eq2 = 1e-00*(v2(t)-v1(t))+1e-03*(v2(t)-v3(t))+1e-09*diff(v2(t)-v3(t),t) == 0;
eq3 = 1e-03*(v3(t)-v2(t))+1e-09*diff(v3(t)-v2(t),t)+1e-03*v3(t) == 0;
eqs = [eq1 eq2 eq3];
vars = [v1 v2 v3];
f = daeFunction(eqs,vars)

This works and gives you a function handle which can be used with ode15i:

f =

  function_handle with value:

    @(t,in2,in3)[in2(1,:)-sin(t.*6.283185307179586e8)./1.0e2;in3(2,:)./1.0e9-in3(3,:)./1.0e9-in2(1,:)+in2(2,:).*1.001-in2(3,:)./1.0e3;in3(2,:).*(-1.0e-9)+in3(3,:)./1.0e9-in2(2,:)./1.0e3+in2(3,:)./5.0e2]

I'm sorry that I notice so late!

Best regards

Stephan

[Stephan]

I think you can only use ode15s or similar solvers like ode23s or ode15i if you follow the workflow given here - maybe this link is also useful. There is a difference between DAE and ODE in Matlab, so that i do not believe that you will be able to use odeToVectorField. I think if you want to solve these kind of problems in Matlab you will have to follow the DAE solving workflow.

But i also think this is not a big problem, since you would also use matlabFunction, once you proceeded with odeToVectorField and the result would also be a function handle that is passed to a numeric solver. In general this is the same procedure but using another tool.

[S H]

Hi Stephen, Thank you for answering my question. You have been extremely helpful. I added ode15i solver to your code and could verify that Matlab solves this circuit properly and shows correct responses at high and low frequencies. Can you tell me if there is a safe and short cut way to define yp0 parameters in ode15i(f,time,y0,yp0). Defining y0 is easy but is there any way to ask Matlab find the yp0 solutions of a system if y0 parameters are supplied (instead of finding yp0 with hand calculation)?

[Stephan]

Did you try decic?

[S H]

I will read about it. Thank you.