1550078481-Ordinary_Differential_Equations__Roberts_

CSODE User's Guide 505

Then we enter the nonzero entries of A in the 2 x 2 array which appears

and which is initially filled with zeros. The entries may be entered as integers,

fixed-point constants, or floating-point constants using E or D exponential

form. To illustrate this feature, we enter a 11 = 1.5 in fixed-point form as 1.5,

a12 = 1 in integer form as 1, a 21 = -2.5 in floating-point form as -.25El,

and az2 = .5 in floating-point form as 5.D - 01. Normally, we would input

the entries of A exactly as they appear in equation (1). After making sure

we have entered the values of A correctly, we click on the VERIFY MATRIX

ENTRIES AND CALCULATE button. This causes a Please Confirm yes/no

box to appear. We clicked yes, since the entries were correct. This causes the

screen shown in Figure A.7 to appear.

Oi EIGEN 1!1~£1

EIGEN finds aU eigenvalues and eigenvectors of a real. square matrix A of order N where 2 <"" N <= 6.

Enler the size of the N x N maltix A. N "' )2 (Aftei you have entered lhe value on N, p1ess the Enle1 key.)

Column 1

Row

,~

2~

(Enter the non-zero entries of the matrix A below.)

2

...... H .. HHH-HOHHHUHHHOH•UOHHOH>-•U<UHOHHH•>H"H-HHmHH""""-""' •rnOHOHHH•HOH•••••-<n0 .. 0-H-HH .. H<••HO-OHH••o•HrnO-•-•••-•<HO•••o•M-HMHHOH'HHOMH-•< •<-•HHOHH'M•HHH'HH .. n<H•OH<•I ;

THE MATRIX tJHOSB EIGENVALUES AND EIGENVECTORS ARE TO BE CALCULATRD IS

l. SOOOB+OO l. OOOOR+OO

-2. SOOOB+OO 5. OOOOB-01

AN EIGENVALUE IS l. OOOOOB+OO t l. SOOOOB+OO I

THE ASSOCIATED EIGENVECTOR IS

6. OOOOOB- 01 t -z. OOOOOB-01 I


7. OOOOOB+OO + l. OOOOOBtOO I
   AN B:ICBNVALUB IS 1. OOOOOE+OO + -L SOOOOB+OO I
   THE ASSOCIATED EIGENITECTOR IS


8. OOOOOE-01 + 2. OOOOOR-01 I
   0.00000B+OO + -1.00000BtOO I

• CALCULATE EIGENVALUES THE
  EIGENVECTORS AND
  OF MATRIX ANEW

Figure A.7 Screen Showing a 2 x 2 Matrix and Its Eigenvalues

and Associated Eigenvectors

For verification purposes, the matrix A with all entries displayed in single
precision, floating-point form appears first in the output list box, followed by
the set of two eigenvalues and associated eigenvectors. From Figure A. 7 we
see that one eigenvalue is ,\ 1 = 1 + l.5i and the associated eigenvector is

X1 -- (·6 -i .2i) ·

The second eigenvalue is >-2 = 1 - l.5i and the associated eigenvector is

Xz - ( .- 6+ · .2i) ·

-i