Agriculture Reference
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Notice that
ξ=β
for
D
fr
=
. Replacing
x
with
i
( )
and substituting
approximation for partial derivatives, (e.g., Equations A2, A3, and B2), into
the above equation and rearranging produces:
j
+
1
j
+
1
j
+
1
Ac
′′′
+ ′′′
Bc
+ ′′′
Cc
= ′′′
E
(D2)
i
−
1
i
i
+
1
where
1
2
Aa vi
D
fr
−
1
′′′ =
ξ
(D3)
4
D
−
1
D
−
2
B
′′′ =− +β−ξ +−
1
v
av i
[
fr
(
Di
1)
fr
]
(D4)
4
fr
1
2
D
−
1
D
−
2
Ca vi
′′′ =
ξ +ξ −
fr
av Di
(
1)
fr
− β
v
(D5)
4
4
fr
1
2
(
)
D
−
1
j
j
j
j
Ec
′′′ =− −
av i
ξ −+
fr
c
2
cc
(D6)
i
4
i
+
1
i
i
−
1
Apparently, Equation D2 reduces to Equation B3 for
D
fr
=
.
References
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