Is there a case where one may prefer a lower order method of numerical integration over a higher order one? Suppose you have a limit for the accuracy you need to acquire. Using, say RK4, will allow you to achive this with less time steps than, say Euler.
Is there a particular scenario where using the Euler method will be more (computationaly) efficient, given the accuracy limit?

Note that RK4 is convergent of order 4 provided that the right-hand side $f$
of the ODE $$\dot{y} = f(t,y)$$ is sufficiently smooth.
If $f$ is only continuously differentiable, RK4 and the explicit Euler method share the same linear convergence rate.
In this case, you might prefer the explicit Euler method.
