Exercise 1

To gain experience with dde23, compute and plot the solution of the following problem from [12]. Solve
y1(t)
=
y5(t-1) + y3(t-1)
y2(t)
=
y1(t-1) + y2(t-0.5)
y3(t)
=
y3(t-1) + y1(t-0.5)
y4(t)
=
y5(t-1) y4(t-1)
y5(t)
=
y1(t-1)
on [0,1] with history y1(t) = exp(t+1), y2(t) = exp(t+0.5), y3(t) = sin(t+1), y4(t) = y1(t), y5(t) = y1(t) for t 0.

In this you will have to evaluate the history in a function and supply its name, say 'exer1h', as the history argument of dde23. Remember that both the ddefile and the history function must return column vectors. In [12] this problem is used to show how to prepare a class of DDEs for solution with DMRODE. You might find it interesting to compare this preparation to what you had to do.

Reference

[12]
K.W. Neves, Automatic integration of functional differential equations: an approach, ACM TOMS, 1 (1975), 357-368.