Table 2 Approximate solutions with \(n=10\) using the presented method for Example 1
| Â | \(w_{1}=w_{2}=1\) | \(w_{1}=1+x\), \(w_{2}=0.1+\sin (\pi x)\) | ||
|---|---|---|---|---|
x | \(y_{{1,10}}(x)\) | \(y_{{2,10}}(x)\) | \(y_{{1,10}}(x)\) | \(y_{{2,10}}(x)\) |
0.0 | 0 | 1 | 0 | 1 |
0.1 | 0.0998334982 | 0.9950042188 | 0.0998333812 | 0.9950038932 |
0.2 | 0.1986684935 | 0.9800655577 | 0.1986690503 | 0.9800660565 |
0.3 | 0.2955209998 | 0.9553361997 | 0.2955198294 | 0.9553357200 |
0.4 | 0.3894199298 | 0.9210614037 | 0.3894180020 | 0.9210599737 |
0.5 | 0.4794260733 | 0.8775836332 | 0.4794256663 | 0.8775813131 |
0.6 | 0.5646418992 | 0.8253370370 | 0.5646429865 | 0.8253341966 |
0.7 | 0.6442169865 | 0.7648422145 | 0.6442174149 | 0.7648405476 |
0.8 | 0.7173554835 | 0.6967045272 | 0.7173544570 | 0.6967046643 |
0.9 | 0.7833263536 | 0.6216087634 | 0.7833258557 | 0.6216074794 |
1.0 | 0.8414701784 | 0.5403006405 | 0.8414695666 | 0.5402994905 |