Exercises

Question 1

Exercise 14

Answer 1

More accurate answer = 118.86

Step size < 0.0937

Question 2

Exercise 21

Answer 2

a = -5

B = 2

c = -1

Question 3

Exercise 22

Answer 3

a = 5

B = 3

c = 1

Question 4

Exercise 23

Answer 4

Possibly done wrong

c - 5000?

Question 5

Exercise 33

Answer 5

2nd iteration

x2 = 10/3

x3 = 8/3

Question 6

Exercise 31

Answer 6

2nd iteration values

a = 4

B = -5

Yes, it is diagonally dominant

Reasonable to assume answer within + or - 2 of actual answer

Question 7

Exercise 32

Answer 7

2nd iteration

a = 7/2

B = -4

Jacobi method is more accurate than Gauss seidel method

Question 8

Exercise 37

Answer 8

8

Question 9

Exercise 25

Answer 9

-24

Question 10

Exercise 42

Answer 10

after 3rd iteration:

a = 2

B = 3

Best estimate 2.5 + - 0.5

Second part not done

Question 11

Exercise 51

Use analytical method

Answer 11

Best estimate x = -2 + or - 256/455

Question 12

Exercise 53

Answer 12

5/3

Question 13

Exercise 61

Answer 13

Using h = 1 as step size, ans = 45

Using h = 2 as step size, ans = 50

Through Romberg Integration I = 43.3

Question 14

Exercise 62

Answer 14

Using h = 1, answer is 410.6

Using h = 2, answer is 426.3

I = 409.6

Question 15

Exercise 63

Answer 15

Final answer y(2) = 22

Question 16

Exercise 64

Answer 16

x(1) = 6.5

Question 17

Exercise 65

Answer 17

y(4) = 70

Question 18

Exercise 81

Answer 18

Y1 = 10

Y2 = 12

Question 19

Exercise 84

The figure should be 100 at each of the top nodes and 0 on boundary

Answer 19

ans =

25 25

6.25 6.25