Question

I’m trying to solve differential equations using ode23 in MATLAB but in the given problem, the value given is different from the endpoint. For example: y’+y=2, y(0)=0, t on [-2,10]. ode23 expects a y0 but in this case, I need y(0)=0 and not y(-2)=0. How can I change the parameters of ode23 so that it still tells me the values on the interval [-2,10] but also with y(0)=0?

Answer 1

You can split your problem and solve

    " y'(t) = f(t,y(t)) on (0,10] , y(0) = 0 "    (a)

and

    " y'(t) = f(t,y(t)) on [-2,0) , y(0) = 0 , "    (b)

where (a) directly fits ode23, while (b) has to be rewritten by a variable transform t := -t to give

    " y'(t) = -f(t,y(t)) on (0,2] , y(0) = 0 . "

As ode23 bases on single step methods, the approach of splitting the integration interval is legit.