Di¤erential Equations and Matrix Algebra I (MA 221), Fall Quarter, 1999-2000
WorkSheet 13
Work with one other person.
1) Apply two steps of the Euler method to
That is, I want an estimate of x(0:2):
dx
= 6 ¡ 2x; x(0) = 5 using a step size of h = 0:1:
dt
2) Explain the improved Euler method to each other. Then after (and only after) everyone
understands the explanations, apply the improved Euler to the DE in (1) to approximate
x(0:2):
3) Compare your approximations in (1) and (2) with the analytic solution of the DE.
dx
= x2 ¡ 3x + 2: Be sure to include the
dt
equilibrium solutions (ie the trivial solutions) and discuss the stability of each.
4) Give a rough sketch of the direction …eld for