(1) x+√y=16, (2) y+√x=11,
Let x0=0 and n=0.
(a) yn=11-√xn, xn+1=16-√yn, yn+1=11-√xn+1
(b) n=n+1, then go to (a)
The following table shows the progression of the iterative process:
n |
xn |
yn |
0 |
0 |
11 |
1 |
12.6834 |
7.4386 |
2 |
13.2726 |
7.3568 |
3 |
13.2877 |
7.3548 |
4 |
13.2880 |
7.3547 |
5 |
13.28804040 |
7.354723549 |
6 |
13.28804064 |
7.354723516 |
7 |
13.28804065 |
7.354723515 |
8 |
13.28804065 |
7.354723515 |
The stability of the last two rows of the table gives us the solution for x and y.