Solving Coupled Differential Equations (in Matlab)

[ksmanis]

Hi,

I have the following problem to solve. My system can be defined as a set of coupled differential equations as described below:

dy/dt = -a*y(t) + b*x(t) + (m-y(t))*r;
dx/dt = a*y(t) - b*x(t) + (n-x(t))*r;

where m,n and r are constants. I have the values of y(t) and x(t) for different values of t. The above dy/dt and dx/dt are based on theoretical interpretation (and I do not have their values). For the given set of x(t), y(t), I would like to find the coefficients 'a' and 'b' fitting the above system.

Appreciate your help in solving this problem in any package (preferably matlab)

Kind Regards
Subbu

 

[pasmith]

The ODE is linear with constant coefficients, so can be solved analytically to obtain $(x,y)(t)$ expressly. One could then attempt to minimize the square error $\sum_i \|(x,y)(t_i) - (x_i,y_i)\|^2$ in the usual way.