Chapter D1.2, Problem 29E

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