u
n
-
a
1
-
a
2
-
1
?
t
u
t
n
a
2
+
ß
1
+
ß
2
-
1
?
t
2
u
t
t
n
-
a
2
2
-
ß
2
-
1
2
?
t
3
u
t
t
t
n
a
2
6
+
ß
2
2
-
1
6
?
t
4
u
t
t
t
t
n
-
a
2
24
-
ß
2
6
-
1
24
\begin{array}{r@{:\: \: }cccccccccc} u^ n &+ & \frac{\beta _2}{2} & - & \frac{1}{6} \\[0.1in & & - & 1 \\[0.1in] {\Delta t}u_ t^ n & & & & \alpha _2 & + & \beta _1 & + & \beta _2 & - & 1 \\[0.1in] {\Delta t}^2 u_{tt}^ n & & & - & \frac{\alpha _2}{2} & & & - & \beta _2 & - & \frac{1}{2} \\[0.1in] {\Delta t}^3 u_{ttt}^ n & & & & \frac{\alpha _2}{6} & & & + & \frac{\beta _2}{2} & - & \frac{1}{6} \\[0.1in] {\Delta t}^4 u_{tttt}^ n & & & -& \frac{\alpha _2}{24} & & & - & \frac{\beta _2}{6} & - & \frac{1}{24} \end{array}
(1.62)