Question

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.

1. Is it linear? Separable?
2. Write down the integral equation using definite integral (without solving it)
3. Considering an real example: v’ = 5 - 0.5v², with v(0)=5.
   1. Use Euler algorithm with h=0.1, find v(0.5)
   2. Use RK4 algorithm with h=0.1, find v(0.5)
   3. 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?

Answer 1