How to solve ODE's in Matrix Form?

Hi,

I have a set of equations like this and am clueless on how to solve on MATLAB and hope someone can help. The intial conditions are P0(0) = 1; P1(0) = 0.

[James Tursa]

The ode45 doc has examples for vector variables. Have you looked at those yet?

[Benjamin Watson]

Hi James Tursa,

I've been trying to get ode45 to work for this example for a few days but had no luck.

Regards

Ben

[James Tursa]

Please post what you have tried and what problems you are having with your code and we can help.

[Benjamin Watson]

Hi James Tursa,

I've finally got it working using the dsolve function but is there anyway for it to solve in symbolically as I have Lam values and Mu values which I've had to input a numerical value for but is there anyway to keep these in sysmbolic form. Also is there anyway to get an output which limits t to infinty? Thanks Ben

syms P0(t) P1(t)
Lam = 2000
Mu = 1000

eqns = [diff(P0,t) == -Lam*P0+Mu*P1,...
    diff(P1,t) == Lam*P0-Mu*P1];

sol = dsolve(eqns, P0(0) == 1, P1(0) == 0)
solP0(t)= sol.P0
solP1(t)= sol.P1

Answer 1

[Star Strider]

For a linear system such as yours, another option is the expm (link) function. It is the term in the solution for a linear system:

where = expm(A*t).

This requires a loop for the inputs and for values of ‘t’, however that is more of an inconvenience than a problem.