ode inside ode ; coupled ode ?

Hi,

my ode requires a solution of another ode. The therm diff(sol.y)/diff(sol.x)/sol.y(end) is needed in the second ode.

for example

 function dvdt=myfun(t,v,...)
 % Calculating the height of the liquid and its derivative
  sol = ode45(f,TSPAN,h,OPTIONS,v,v0,uclose,Au,dw);   
        h_nm1=h_n;
        h_n=sol.y(end);
        dh=diff(sol.y)./diff(sol.y);

 % my ode MOL discretization calculating the concentration of particles

 i=1
 dvdt=...
i=2:N-1
dvdt=...
i=N
dvdt=...

Two Questions:

I do not need to solve the first ode always from zero. So i could use the old solution as initial conditions and the old time like TSPAN=[told t] ?

The way i am solving it makes me somehow uncomfortable. I am sure there is a better way. Could i solve both odes at once? But still the second one needs the solution of the first one. So it would be better to set them up as coupled ODES ?

I know you could answer those questions with "yes" or "no", but please comment an that.

Moritz

[Moritz]

well i should say, that the first ode is a simple ode. The second one is a pde discretized with MOL.

I need to calculate the height of the interface h(t) and use diff(h(t)/h(t) in the pde. Since my discretization is different for both odes i do not know how to code that the best way.

The first ode needs only the last point of the pde. This point is updated with every timestep. So do i need to use global variables here ? Or can i pass the solution of the pde to the ode as an argument ? While calling the ode at the every call of the pde ?

[RahulTandon]

Could you please provide the two basic equations, to start with. The approach here is different!

Answer 1

[Torsten]

Solve the (N+1) ODEs simultaneously in one call to ODE15s:

dv(1)/dt = ...
dv(2)/dt = ...
...
dv(N)/dt = ...
+
dh/dt = ...

Best wishes

Torsten.