1540470959-Boundary_Value_Problems_and_Partial_Differential_Equations__Powers

494 Answers to Odd-Numbered Exercises

First Problem Second Problem

ii

m 0123401234

0 0111001110

1 0 2 / 31 2 / 3 001 / 32 / 31 / 3 0

2 0 5 / 97 / 95 / 9 002 / 92 / 92 / 9 0

3 0 14 / 27 17 / 27 14 / 27 002 / 27 4 / 27 2 / 27 0

4 0 31 / 81 45 / 81 31 / 81 004 / 81 4 / 81 4 / 81 0

9.ui(m+ 1 )=(ui+ 1 (m)+ui− 1 (m))/2.

i

m 01 2 3 4 5

0 00 0 0 0 0

1 1 / 2 00000

2 1 1 /40 0 00

3 3 / 2 1 / 21 / 80 0 0

4 2 13 / 16 1 / 41 / 16 0 0

5 5 / 2 9 / 87 / 16 1 / 81 / 32 0

6 3 87 / 32 5 / 815 / 64 1 / 16 0

11.

i

m 01234

0 00000

1 0 0001

2 0 0011

3 0 0111

4 0 1111

5 0 1111

6 0 0111

7 0 0011

8 0 0001

13. Letuij∼=u(xi,yj).Thenu 11 =u 22 =u 33 = 0 .5,u 12 = 0 .698,u 13 = 0 .792,
    u 21 = 0 .302,u 23 = 0 .624,u 21 = 0 .209,u 32 = 0 .376.


14. NumberasinChapter7,Fig.4.Thenu 1 =u 3 =u 7 =u 9 andu 2 =u 4 =
    u 6 =u 8.

m

01 2 3 4 5

u 1 1 1 / 23 / 81 / 43 / 16 1 / 8

u 2 1 3 / 41 / 23 / 81 / 43 / 16

u 5 1 13 / 41 / 23 / 81 / 4