solve a differential equation at specific points

I have this differential equation (attached .jpg file). I also have the 'gamma', 'u' and 'tau' values (attached unotfinder.m file)

I need to find 'u_0' values that satisfy the equation. Can anyone suggest a way to do this?

Answer 1

[Erik Keever]

The equation given, (d gamma / d u)|_{u=u0} = tau, doesn't define a differential equation for gamma, it defines a boundary condition: gamma dot = tau at u=u0.

If you mean you've got discrete lists of [tau_i gamma_i], Matlab's interp1 will create the appearance of a smooth function that can then be used with e.g. fzero to search for the zero.

Matlab's ODE solvers will give output for specific times if you specify them,

   [tout, yout] = ode*(odefun, [t0 t1 t2 ... tfinal], y0)

where the vector of t_i are monotonically increasing or decreasing (see doc ode45 for more)

[Anik Faisal]

thanks!