CSODE User's Guide 521In order to use SOLVESYS to solve the system IVP (3), we double click the
CSODE icon and when the program selection screen appears on the monitor,
we single click the SOLVESYS button. Since the system (3) has two com-ponents, after "N = " we enter 2 and press the Enter key. Next, we enter
the interval of integration [a, b] and the initial value c which must be in the
interval. Since, in this case, the interval of integration is [O, 2.5], we input
after "a = " the value 0 and input after "b = " the value 2.5. Since the initial
conditions in (3) are specified at 0, after "c = " we input 0 and click the
VERIFY a, b, and c button. Next, we enter the system defining functions,
as they appear on the monitor. First, in the box after "y'l = Fl = " we
enter 3 y2 - 2 yr2 - 1 and press the Enter key. Then in the box after
"y'2 = F2 = " we enter 8 * yl - y2~2 - 7 and press the Enter key. Next,
we enter the values for the initial conditions y 1 (0) = 2, y 2 (0) = 0. We have
already input the value of c = 0. Since y 1 (0) = 2 = d 1 , after "dl = " we
input 2. Since Y2(0) = 0 = d2, we do not need to change the default value
of 0 which appears after "d2 = ", so we click the VERIFY INITIAL VAL-
UES AND INTEGRATE button. A set of options appears. The first option,
Graph solution components, is already selected, so we click the OK button.
Check boxes for yl and y2 appear. Since we want to graph both solution
components, we click the box before yl and the box before y2 and then click
OK An Information for Graphing box appears. After reading the contents of
the box, we click OK Since SOLVEIVP was able to integrate over the entire
interval [O, 2.5], Xmin = 0 and Xmax = 2.5. We do not wish to change these
values. Ymin = 0 and Ymax = 2.743130. We decided to change Ymax to
5 to produce the graph. After changing the value of Ymax to 5, we click
the VERIFY XMIN, XMAX, YMIN, YMAX button. This causes the graph
shown in Figure A.15 to appear on the monitor. Observe that the color of the
solution components appearing in the graph on the monitor are li sted at the
bottom of the graph- yl is black, y2 is blue, etc.
We still want to produce a phase-plane graph of y(t) versus x(t)- that is ,
y 2 (x) versus y 1 (x), so we click the OPTIONS button at the upper right corner
of the graph. This causes the set of options to reappear. We select the second
option, PHASE-PLANE graph, and click OK The program needs to know
which component we want to be the horizontal axis and which component
we want to be the vertical axis. By default, the horizontal axis is selected
to be component 1 of the system IVP and the vertical axis is selected to be
component 2. Since this is the way we wish to view the phase-plane graph,
we simply click OK
[NOTES: If we wanted a phase-plane graph of yl versus y2, we would
input in the box after "IH = " the value 2 and in the box after "IV = " the
value 1. For a system with n components where 2 ::::; n ::::; 6, any i satisfying
1 ::::; i ::::; n may be chosen for the horizontal axis and entered after "IH = "
and any j =f. i satisfying 1 ::::; j ::::; n may be chosen for the vertical axis.]