Assignment #9
Due Friday 12/13
From text (Cheney&Kincaid, 4th ed.):
Read introduction to chapter 8: "Initial
value problem: Analytical versus numerical solution"
§8.1: Problems: # 1ace, 2abc, 3d, 5, 8, 11
§8.1: Computer Problems: # 4b, 5 [Use Euler method as well
as Taylor order 5--write short Matlab codes for both.]
§8.2: Problems: # 3, 9, 11
[§8.2: Computer Problems:] First write a Matlab version
of the RK4 pseudocode listed on pp. 387-388---call it "rk4.m". Then
do the following:
problem A: Use rk4.m and n = 20 steps to approximately
solve
(i) x' = 1+ x^2 , x(0)=0
for x(1)
(ii) x'=-x+sin t, x(0)=1
for x(10).
problem B: Compare the result from A (in both parts) to the
result from Taylor order 5 (see above) and to the exact
solutions.
[§8.3: Computer Problems:]
problem C: Solve A (both parts) using Matlab's
"ode45". Produce one plot for (i) which has all four solutions (rk4,
exact, Taylor O(5), ode45) and errors. Do the same for (ii).
Office: Chapman 301C. Office
hours online. Contact: 474-7693, ffelb@uaf.edu , www.math.uaf.edu/~bueler/