How to solve an ODE with external time-varying source?

Hi,

I am trying to numerically solve y(t) from an equation with the following form:

f is a function of x(t), x(t) is a given set of time-varying values stored in a line vector, [x1 x2 x3 ... xn]. x(t) is the solution of a DDE so I do not think it has any analytic expressions.

My problems are:

Can I turn the line vector into a function of t and just insert that function? If yes, how should I do; if no, is there any other ways to solve the equation?

Thank you.

Answer 1

[Torsten]

a) Save [t1 t2 ... tn], [x1 x2 ... xn] in two arrays T and X.

b) Pass T and X to the integrator:

[tsim,ysim] = ode45(@(t,y)fun(t,y,T,X),tspan,y0)

c) Define the ODE in function "fun":

function dy = fun(t,y,T,X)
  source = interp1(T,X,t)
  source = f(source);
  dy = (source-y)/tau
end

[Cheng Li]

Got it! Thank you