190 ◾ System Instantaneous Availability
where
∫
∫
{}
()
=+≤= =
=+ =+
=+
() 1– ()
() ()*()()
() () (– )()()()* ()
1– () (– )(–) .
0
0
Rt Ft
PX Yt Ft Gt qudu
At Rt At udQu Rt Qt At
fsds At ufusgsds du
t
t
tut
With the numerical solution, approximate values u
1
, u
2
, …, u
N
of u(t
1
),
u(t
2
), …, u(t
N
) in position function u(t) can be solved for a series of discrete points
t
1
, t
2
, …, t
N
. e discrete values t
1
, t
2
, …, t
N
of the independent variable t are
predefined; t
j
is the general equally spaced node, that is, t
1
= t
0
+ h, t
2
= t
0
+ 2h, …,
t
N
= t
0
+ Nh, where h > 0 is called the step length that may vary when necessary;
whereas u
1
, u
2
, …, u
N
is generally called the numerical solution of the initial value
problem [76].
Setting t
0
= 0, and t
1
= t
0
+ h, t
2
= ...