Errors in Euler’s method Consider the following initial value problems.

a.    Find the approximations to y(0, 2) and y(0.4) using Euler’s method with time steps of Δt = 0.2, 0.1, 0.05, and 0.025.

b.    Using the exact solution given, compute the errors in the Euler approximations at t = 0.2 and t = 0.4.

c.    Which time step results in the more accurate approximation? Explain your observations.

d.    In general, how does halving the time step affect the error at t = 0.2 and t = 0.4?

29.    y’(t) = –y, y(0) = 1; y(t) = e^–t