Appendix B
PORTRAIT User's Guide
PORTRAIT is a computer program written in Microsoft Visual Basic 6
designed to execute in the Microsoft Windows environment. The software
PORTRAIT is on the computer disc which accompanies this text. All you
need to do is copy PORTRAIT onto your desktop. Then to run PORTRAIT
double click on the PORTRAIT icon.
For 1 :'::: i :'::: 10, PORTRAIT will attempt to solve numerically the i initial
value problems consisting of the autonomous, two component system initial
value problem
dy1
di = Ji (Y1, Y2);
(1)
dy2
di = f2(y1, Y2);and the initial conditions yl(ci) = d 1 i , y2(ci) = d2i on the interval [ai, bi]
where Ci E [ai, bi]. After the solution of an initial value problem has been
calculated, you may elect for any initial value problem already solved (i) to
print the solution components on the monitor, (ii) to graph any subset of the
solution components in a rectangle R where ai :'::: x :'::: bi and YMIN :'::: y :':::
YMAX where you select the values for YMIN and YMAX, (iii) to produce a
phase-plane portrait of any subset of IVPs already solved on any rectangle,
(iv) to rerun the most recent initial value problem using a different interval
of integration or initial conditions, or (v) input the initial conditions for the
next initial value problem to be solved.
In order to run PORTRAIT, you need to know how to enter integers and
real numbers into the program, how to enter functions into the program in
the syntax of BASIC, and how to read output of the program. In BASIC,
an integer constant is an integer between -32768 and 32767 written with no
commas and no decimal point. Real constants appear in two varieties- fixed-
point constants and floating-point constants. Both contain a decimal point
(usually) and no commas. For example, 3.14159 is a fixed-point constant, six
digit approximation for 7f. A floating-point constant consists of an integer
constant or fixed-point constant followed by the letter E (for single precision)
or D (for double precision) and a signed integer (the exponent). For exam-
ple, 234E5 is a single precision, floating-point representation for the number
- And 314159E-5, 314.159E-02, 0.00314159E+3, and .00314159E3
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