Page 571 - Modelling in Transport Phenomena A Conceptual Approach

B.2. SECONDORDER LINEAR DFFEREXTIAL EQUATIONS

with the initial conditions
Yo = 1
Zo = 0
Choosing h = 0.05, the values of y1 and z1 are calculated as follows:

kl = h f (Yo, 20)
= (0.05)(-0.4)(1) = -0.0200

el = hS(Y0,+4
= (0.05)(0.7)(1- 1 - 0)(1 - 0) = 0

= (0.05)(-0.4) 1 - - -0.0198
=
,
.
) ( O
,
[ ( o*o?) 1
-
0
= (0.05)(0.7) 1 - 1 - - (1 - 0) = 3.5 x

= (0.05)(- 0.4) 1 - - - 0.0198
=
( 0*0:g8>

-
= (0.05)(0.7) [ 1 - ( 1 - - 3.5 x 2 10-41 ( 1-
0.0:")
2
= 3.4032 x low4 (23)

h = hg(Yo+k3,Zo+l3)
= (0.05)(0.7) [l - (1 - 0.0198) - 3.4032 x lov4] (1 - 3.4032 x
= 6.8086 x (25)