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.