Exercise 6

The ARCHI manual [17] provides a sample program for solving

y1¢(t) = y1(t-1)  y2(t-2) y2¢(t) = -y1(t)  y2(t-2)

on [0,4] with history y₁(t) = cos(t),y₂(t) = sin(t) for t < 0 and initial values y₁(0) = 0,y₂(0) = 0 . Notice that y₁(t) is discontinuous at the initial point. For practice, compute and plot the solution. The sample program specifies a pure absolute error of 10^-9. dde23 does not permit a pure absolute error, but for practice with options, use the default relative error tolerance and set 'AbsTol' to 1e-9. You might find it interesting to compare your program to the sample in [17].

Reference

[17]

C.A.H. Paul, A user-guide to Archi, Numer. Anal. Rept. No. 283, Maths. Dept., Univ. of Manchester, U.K., 1995.