
Since Equation 1.23 is only approximate, H(t) is replaced by H
A
(t) to distinguish it from the actual
solution H(t). From Equation 1.23 with H(t) replaced by H
A
(t),
H
A
(t þ Dt) ¼ 1
Dt
AR
H
A
(t) þ
Dt
A
F
1
(t)(1:24)
Equation 1.24 is a difference equation that can be solved for the approximate solution H
A
(t) when
F
1
(t), t 0 and H
A
(0) are known. As we shall see, the approximate solution H
A
(t) can only be
determined at discrete times, namely, t ¼0, Dt,2Dt,3Dt,....
1.3.1 RECURSIVE SOLUTIONS
Difference equations are easily solved because of their inherent structure. The solution values
H
A
(nDt), n ¼1, 2, 3, . . . are obtained in a sequential fashion by repeat