Chapter D1, Problem 21RE

Euler’s method Consider the initial value problem

   $y^{\prime }(t)=\frac{1}{2y},y(0)=1$.

a.    Use Euler’s method with Δt = 0.1 to compute approximations to y(0.1) and y(0.2).

b.    Use Euler’s method with Δt = 0.05 to compute approximations to y(0.1) and y(0.2).

c.    The exact solution of this initial value problem is $y=\sqrt{t+1}$. Compute the errors in the approximations to y(0.2) found in parts (a) and (b). Which approximation gives the smaller error?