Research Article
On the Solution of Quadratic Nonlinear Integral Equation with Different Singular Kernels
Table 1
Comparison between the Toeplitz matrix method and Nystrom method in different time when kernel takes logarithmic form.
| | | Toeplitz matrix method | Nystrom method | | T | x | | Error | | Error |
| | 0.009 | –0.87 | 0.0000613 | 2.630 × 10−15 | 0.0000613 | 4.950 × 10−15 | | –0.37 | 0.0000111 | 2.157 × 10−15 | 0.0000111 | 8.298 × 10−15 | | 0.13 | 0.0000015 | 1.637 × 10−7 | 0.0000015 | 1.642 × 10−7 | | 0.63 | 0.0000321 | 1.219 × 10−14 | 0.0000321 | 4.992 × 10−15 | | 0.9 | 0.0000656 | 5.469 × 10−15 | 0.0000656 | 1.139 × 10−14 |
| | 0.02 | –0.87 | 0.0003028 | 1.179 × 10−13 | 0.0003028 | 4.435 × 10−13 | | –0.37 | 0.0000548 | 5.055 × 10−14 | 0.0000548 | 2.952 × 10−13 | | 0.13 | 0.0000068 | 9.062 × 10−12 | 0.0000068 | 9.582 × 10−12 | | 0.63 | 0.0001588 | 1.417 × 10−13 | 0.0001588 | 3.315 × 10−13 | | 0.9 | 0.0003240 | 6.330 × 10−15 | 0.0003240 | 3.040 × 10−13 |
| | 0.8 | –0.87 | 0.4844307 | 1.468 × 10−5 | 0.4844625 | 4.647 × 10−5 | | –0.37 | 0.0876232 | 7.192 × 10−6 | 0.0876449 | 2.889 × 10−5 | | 0.13 | 0.0108114 | 4.647 × 10−6 | 0.0108321 | 1.606 × 10−5 | | 0.63 | 0.2540051 | 1.094 × 10−5 | 0.2540541 | 3.807 × 10−5 | | 0.9 | 0.5183947 | 5.367 × 10−6 | 0.5184301 | 3.009 × 10−5 |
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