Shooting methods are employed to obtain solutions of the three-point boundary value problem for the second order equation,
y
=
f
(
x
,
y
,
y
′
)
,
y =f(x,y,y’),
y
(
x
1
)
=
y
1
,
y
(
x
3
)
−
y
(
x
2
)
=
y
2
,
y(x_1)=y_1, \ y(x_{3}) - y(x_2)=y_2,
where
f
:
(
a
,
b
)
×
R
2
→
R
f: (a,b) \times \mathbb R^2 \to \mathbb R
is continuous,
a
>
x
1
>
x
2
>
x
3
>
b
,
a > x_1 > x_2 > x_3 > b,
and
y
1
,
y
2
∈
R
,
y_1,y_2 \in \mathbb R,
and conditions are imposed implying that solutions of such problems are unique, when they exist.