The table here demonstrates the convergence as a function of the number of iterations or time steps. After twelve iterations we have reached the exact value with six leading digits.
Iteration | \( w_1 \) | \( w_2 \) | \( w_3 \) | \( w_4 \) |
0 | 1.000000 | 0.000000 | 0.000000 | 0.000000 |
1 | 0.250000 | 0.500000 | 0.000000 | 0.250000 |
2 | 0.201389 | 0.319444 | 0.055556 | 0.423611 |
3 | 0.247878 | 0.312886 | 0.056327 | 0.382909 |
4 | 0.245494 | 0.321106 | 0.055888 | 0.377513 |
5 | 0.243847 | 0.319941 | 0.056636 | 0.379575 |
6 | 0.244274 | 0.319547 | 0.056788 | 0.379391 |
7 | 0.244333 | 0.319611 | 0.056801 | 0.379255 |
8 | 0.244314 | 0.319610 | 0.056813 | 0.379264 |
9 | 0.244317 | 0.319603 | 0.056817 | 0.379264 |
10 | 0.244318 | 0.319602 | 0.056818 | 0.379262 |
11 | 0.244318 | 0.319602 | 0.056818 | 0.379261 |
12 | 0.244318 | 0.319602 | 0.056818 | 0.379261 |
\( \hat{w}(t=\infty) \) | 0.244318 | 0.319602 | 0.056818 | 0.379261 |