1.Section 8.2.4 describes a geometric interpretation of the Forward Euler method. This exercise will demonstrate the geometric construction of the solution in detail. Consider the differential equation u
= u with u(0) = 1. We use time steps Δt = 1. a) Start at t = 0 and draw a straight line with slope u
(0) = u(0) = 1. Go one time step forward to t = Δt and mark the solution point on the line. b) Draw a straight line through the solution point (Δt, u1) with slope u
(Δt) = u1. Go one time step forward to t = 2Δt and mark the solution point on the line. c) Draw a straight line through the solution point (2Δt, u2) with slope u
(2Δt) = u2. Go one time step forward to t = 3Δt and mark the solution point on the line. d) Set up the Forward Euler scheme for the problem u
= u. Calculate u1, u2, and u3. Check that the numbers are the same as obtained in a)-c).
