Hi, i need some help on this second-order ODE equation:
mu'' + f(u') + s(u) = F(t), t > 0, u(0) = U0, u'(0) = V0
How would it look like as a first-order system?
hey mate,
there are numerous ways to achieve this, but would probably be the simplest way is to let
w(t) = u'(t) --> w'(t) = u''(t)
Thus,
mu''(t)+f(u'(t)) + s(u(t)) = F(t) becomes,
mw'(t) + f(w(t)) + u(t) = F(t) , u(0) = U0 u'(0) = w(0) = V0
here we observe, we have reduced the order of the differential equation, and our system becomes,
mw'(t) + f(w(t)) + u(t) = F(t)
w(t) - u'(t) = 0
Subject to, u(0) = U0 , w(0) = V0
Hope this helps,
let me know if you require any further assistance,
Regards,
David