Chapter 7 493
Chapter 7 Miscellaneous Exercises
- ui+^1 −( ^2 uxi) 2 +ui−^1 −
√
24 xiui=0,i= 0 , 1 ,2,
u 1 −u− 1
2 x =1,u^3 =1;− 18 u 0 + 18 u 1 = 6 ,
9 u 0 − 20. 83 u 1 + 9 u 2 = 0 ,
9 u 1 − 22 u 2 =− 9 ,u 0 =− 0 .248,u 1 = 0 .08,u 2 = 0 .44.3.ui+ 1 − 2 ui+ui− 1
( x)^2 +1
1 +xiui+ 1 −ui− 1
2 x =−(^1 +xi),
i= 1 , 2 , 3 ;u 0 = 1 ,u 4 =0;− 32 u 1 + 17. 60 u 2 =− 15. 65 ,
14. 67 u 1 − 32 u 2 + 17. 33 u 3 =− 1. 5 ,
14. 86 u 2 − 32 u 3 =− 1. 75 ,u 1 = 0 .822,u 2 = 0 .606,u 3 = 0 .335.
5.ui(m+ 1 )=(ui− 1 (m)+ui+ 1 (m))/2. Note that u 3 (m)=u 1 (m)and
u 4 (m)=u 0 (m).i
m 01 2
0 00 0
10.030 0
2 0.06 0.015 0
3 0.09 0.03 0.15
4 0.12 0.053 0.03
5 0.14 0.075 0.053
6 0.17 0.1 0.075
7 0.20 0.122 0.10
8 0.22 0.15 0.122- First problem:ui(m+ 1 )=(ui+ 1 (m)+ui(m)+ui− 1 (m))/3; second prob-
lem:ui(m+ 1 )=(ui+ 1 (m)+ui− 1 (m))/3.