ODE with discrete, external input

Hi everybody, I want to solve a simple ODE for specific discrete time points in which constats are updated externally for each specific t value. vgr

t=1:100; dy/dt=kt;

where k is a external vector with length=length(t) and wich is considered in the equation for each t.... any help? thanks in advance

Answer 1

[Arnaud Miege]

Look at the third example on the ode solver documentation.

HTH,

Arnaud

[Mario Trevino]

thanks, I found the same hint in the ode faqs.

It works

[Sergio]

Hi Arnaud Miege, what would you suggest if the discrete ODE is a (2x2) system? Expanding the first question

t=0:0.02:1;
dxdt = Constant*K1;
dydt = Constant*K2;

where K1 and K2 are both external vector with length=length(t)? and both depending of two variables (x,y)?

Interp1 from matlab would be wrong since we would be interpolating in one dimension while the system is 2D.

Answer 2

[Torsten]

Use

http://www.mathworks.de/help/matlab/ref/griddata.html

if K1 and K2 don't depend explicitly on t, but on the dependent variables x and y.

Best wishes

Torsten.

[Sergio]

Hi Torsten, thanks for your answer! K1, K2 don't depend on t(!) that is correct! I have cheked the griddata, could you give a more concrete example in how I can implement this (griddata)

To use griddata from matlab:

   vq = griddata(x,y,v,xq,yq)

I need: x,y,v and xq,yq are the query points right? I have x,y and v, but when I try griddata in matlab I get:

Undefined function or variable 'xq'

Thanks!

[Torsten]

I guess your dependent variables y(1) and y(2) from the ODE integrator are the xq and yq variables, aren't they?

So you have to call griddata like

K1=griddata(xK1,yK1,vK1,y(1),y(2))

K2=griddata(xK2,yK2,vK2,y(1),y(2))

if vK1 is your given vector of K1 values at points (xK1,yK1) and vK2 is your given vector of K2 values at points (xK2,yK2).

Best wishes

Torsten.

[Sergio]

Thanks! but I still don't understand! Sorry!

I have another example here which is more easier but which can help me to understand.

Assume I have:

    x1 = 40:0.005:55;
    x1=x1';
    x2=40:0.005:55;
    x2=x2';

And then I discretize the following function:

    V1=x1.*(0.2-0.005*x2);
    V2=x2.*(-0.5+0.01*x1);

How can I use griddata now? And how can I solve this as an ODE?

[Torsten]

Sorry, but meanwhile, I don't understand what you are trying to do.

Please specify more clearly:

What is the ODE you are trying to solve ?

Which MATLAB program are you trying to use to solve your ODE ?

Which kind of external input data do you have and where do they enter the ODE ?

Best wishes

Torsten.