41
where
Ml = {2ukU + ij(yh-) + i = (1+¡?(^))5 (3'60)
rifr-7*)i(l+p^^)* (3.61)
Booij points out that the splitting matrix approach employed by Radder (1979) is equivalent
to the choice
1R = *(1 + 2k2[p-U2])
£r = ki(p-U2)2
Using the results (3.60) and (3.61) in Eq. (3.46) along with the definition (3.49) gives the
parabolic equation
(1 +
M
k2{p- U2)
By expanding the pseudo-operators in the form
M
^ <£+j = tkk*(p U2)* ^1 +
M
k2(p-U2)
v 2
J 4 ^+(3.62)
(
1 +
1 +
i)> (i +
M
k2(p U2)J \ 4k2{p-U2)
M \* .. /_ 3 M
iYi+ (i+¡¡
)*+
k2(pU2)) \ 4 k2{p U2)j
the result of both expansions may be summarized in the general equation
(3.63)
(3.64)
fz{kib- ( + kfr-lu*)) +} = V)1 0 + to-U>)) ** (3'65)