1550078481-Ordinary_Differential_Equations__Roberts_

528 Ordinary Differential Equations

ii Computer Solution of Ordma1y 011ferenhal Equations by Charles Roberts 1!11!1 Ei

I RUN i

iPORTRAITi

i·-····--··-)

Portrait solves the autonomous. 2 component

vector initial value problem:

yl' =fl (yl. y2)

y2' = f2(yl. y2)

for 1 <= i <= 10 initial conditions: yl (ci) = dl i. y2(ci) = d2i

where ci is in the interval of integration [ai. bi].

And Portrait produces a phase plane graph of

y2 (vertical axis) versus yl (horizontal axis).

Figure B.1 PORTRAIT Introduction Screen

ii PORTRAIT ~l!J£i

Enter the system delining functions Fl, F2

y'l =Fl=

Wter ioo hove entered lhe function Fl. 111ess the Enter key.)

Figure B.2 PORTRAIT System Definition Screen

First, we enter the system defining functions as they appear on the monitor.

In the box aft er "y'l =Fl=" we enter yl-.5y1y2 and press the Enter key.

When "y'2 = F2 =" appears on the monitor, we enter -2 * y2 + .25 * yl * y2

in the box after it and press the Enter key. Since we are going to solve a total

of two initial value problems, in the box after "N = " we enter 2 and press

the Enter key. Since for (i) the interval of integration is [O, 4 .5] and the initial

conditions are Y1 (0) = 5 and Y2 (0) = 5, in the box under bi = we enter 4.5,

in the box under dli = we enter 5, and in the box under d2i = we enter 5.

(NOTE: There is no need to enter the value of 0 for ai or Ci, since these are

the default values.)

At this point the monitor looks like the screen displayed in Figure B.3.