For objects falling into water or other situations, the
resistance may be proportional to v2 as in mv’ = ma –
kv2, v(0) = v0, as usual m, a, and k are
constants.
- Is it linear? Separable?
- Write down the integral equation using definite integral
(without solving it)
- Considering an real example: v’ = 5 - 0.5v2, with
v(0)=5.
- Use Euler algorithm with h=0.1, find v(0.5)
- Use RK4 algorithm with h=0.1, find v(0.5)
- After solving the equation we have the true value v(0.5) =
3.4712, what are the relative errors in % for Euler and RK4
algorithm?