MATLAB: Simulation of a coupled ODE-transport PDE system

odeode-pdepde

Hi all!

The considered system is coupling an ordinary differential equation and a transport equation with potential term. The system is given by :

   DX/Dt = A*X(t) + B*z(1,t)
   dz(x,t)/dx + c*dz(x,t)/dt + h*z(x,t) = 0
   z(0,t) = C*X(t) + D*z(1,t)
   z(x,0) = z0
   X(t=0) = X0

I want to simulate this system on Matlab, but I don't really know how to do it. I've already tested the Matlab function Pdedp but it doesn't work for this kind of systems. Thank you for your help!

Best Answer

There are no ready-to-use MATLAB tools available for your system of equations.

Discretize the PDE (2nd equation) in space and use ODE15S to solve the resulting system of ordinary differential equations (1st and 2nd equation).

Look up "method-of-lines" for more details.

Best wishes

Torsten.

Related Solutions

MATLAB: Solving a coupled system of differential equations with matrix form!!

Sure,

Lets introduce a new variable z such that

z(1) = y;
z(2) = v;

Then we have for Dz:

Dz(1) = z(2);
Dz(2) = -a*z(1);

Then you write your ODE-function (preferably in an m-file):

function Dy = harmonic_ode(t,z)
Dz = [0;0];
Dz(1) = z(2);
Dz(2) = -a*z(1);

To solve your ODE you should preferably use one of the built-in ODE-solvers, for example ode23 z0 = [y0;y1]; [sol] = ode23(@(t,z) harmonic_ode(t,z),t_span,z0);

HTH

MATLAB: How to solve boundary condition with ordinary differential in PDEPE

PDEPE does not accept ordinary differential equations as boundary conditions.

In the case above, you can simply integrate the ODEs beforehand and supply

C(0,t) = C(0)*(1+alpha*t)
C(1,t) = C(1)*(1+alpha*t)

But if the ODEs for the boundaries get more complicated, you will have to code the solution of the PDE on your own.

One way is to discretize the PDE in space and solve the resulting system of ordinary differential equations using ODE15S. Look up "method-of-lines" for more details.